hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Multiplicative order
In number theory, given a positive integer n and an integer a coprime to n, the multiplicative order of a modulo n is the smallest positive integer k such that .

In other words, the multiplicative order of a modulo n is the order of a in the multiplicative group of the units in the ring of the integers modulo n.

The order of a modulo n is sometimes written as .

Order (group theory)
In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of an element of a group (also called period length or period) is the order of the subgroup generated by the element. If the group operation is denoted as a multiplication, the order of an element a of a group, is thus the smallest positive integer m such that am = e, where e denotes the identity element of the group, and am denotes the product of m copies of a. If no such m exists, the order of a is infinite.

The order of a group G is denoted by ord(G) or |G|, and the order of an element a is denoted by ord(a) or |a|, instead of  where the brackets denote the generated group.

Lagrange's theorem states that for any subgroup H of a finite group G, the order of the subgroup divides the order of the group; that is, |H| is a divisor of |G|. In particular, the order |a| of any element is a divisor of |G|.
Unaspis citri
Unaspis citri, known generally as citrus snow scale, is a species of armored scale insect in the family Diaspididae. Other common names include the orange chionaspi, orange snow scale, white louse scale, and white snow scale.

Diaspididae
Diaspididae is the largest family of scale insects with over 2650 described species in around 400 genera. As with all scale insects, the female produces a waxy protective scale beneath which it feeds on its host plant. Diaspidid scales are far more substantial than those of most other families, incorporating the exuviae from the first two nymphal instars and sometimes faecal matter and fragments of the host plant. These can be complex and extremely waterproof structures rather resembling a suit of armor. For this reason these insects are commonly referred to as armored scale insects. As it is so robust and firmly attached to the host plant, the scale often persists long after the insect has died.

Some African Diaspididae are attended by ants of genus Melissotarsus. The ants appear to consume the armored scales because Diaspididae are completely naked when ant-attended; the ant nest itself remains completely hidden under the bark of the tree.
Division of Greenway
The Division of Greenway is an Australian electoral division in the state of New South Wales. It is located in Sydney's west and northwestern suburbs and includes parts of the Blacktown City Council and The Hills Shire. It is currently represented by Labor MP Michelle Rowland.

Greenway is a relatively diverse electorate, with a large Indian community and smaller immigrant communities of Filipino and Sri Lankan ancestry. According to the 2016 census, only 54.5% of electors were born in Australia, while 11% were born in India.

Blacktown City Council
Blacktown City Council is a local government area in Western Sydney, situated on the Cumberland Plain, approximately 35 kilometres (22 mi) west of the Sydney central business district, in the state of New South Wales, Australia. Established in 1906 as the Blacktown Shire and becoming the Municipality of Blacktown in 1961 before gaining city status in 1979, the City occupies an area of 246.9 square kilometres (95.3 sq mi) and has a population of 410,419, making it the most populous local government area in Sydney. It is a member council of the Hawkesbury River County Council.

The Mayor of Blacktown City Council is Councillor Brad Bunting following the death of then-mayor Tony Bleasdale OAM, a member of the Australian Labor Party who died 3 May 2024.
HMS Truant (1918)
HMS Truant was an S-class destroyer, which served with the Royal Navy. The vessel was the first of the name to enter service in the navy. Launched on 18 September 1918, Truant was too late to see service in the First World War, and, instead of joining the Grand Fleet, the vessel was allocated to Portsmouth to be a tender to HMS Victory. The vessel's subsequent time in service was relatively uneventful, despite gaining a reputation as the fastest destroyer in the fleet, capable of up to 37 knots (69 km/h; 43 mph). However, in 1921, the destroyer became the control ship for the radio-controlled target ship Agamemnon and, in 1923, a similar role with smaller Coastal Motor Boats. This service did not last long. The signing of the London Naval Treaty sounded the death knell for the ship as it limited the destroyer tonnage that the Royal Navy could operate. As newer and more powerful destroyers entered service, Truant was retired on 28 November 1931 and broken up.

S-class destroyer (1917)
The S class (initially known as the Modified Trenchant class) was a class of 67 destroyers ordered for the Royal Navy in 1917 under the 11th and 12th Emergency War Programmes. They saw active service in the last months of the First World War and in the Russian and Irish Civil Wars during the early 1920s.  Most were relegated to the reserve by the mid-1920s and subsequently scrapped under the terms of the London Naval Treaty. Eleven survivors saw much action during the Second World War.
Underground (role-playing game)
Underground is a satirical "grim and gritty"-style superhero role playing game set in the near future. It was released by Mayfair Games in 1993 as a commentary on the politics and society of the early 1990s as expressed through the year 2021.

Modern Age of Comic Books
The Modern Age of Comic Books is a period in the history of American superhero comic books which began in 1985 and continues through the present day. During approximately the first 15 years of this period, many comic book characters were redesigned, creators gained prominence in the industry, independent comics flourished, and larger publishing houses became more commercialized.

A common alternative name for this period is the Dark Age of Comic Books, due to the popularity and artistic influence of titles with serious content, such as Batman: The Dark Knight Returns and Watchmen.
Ferdinand Maximilian, Prince of Ysenburg-Büdingen-Wächtersbach
Ferdinand Maximilian III of Ysenburg-Wächtersbach (24 October 1824 – 5 June 1903) was the head of the Wächtersbach branch of the House of Ysenburg and the first Prince of Isenburg-Budingen-Wächtersbach.

County of Isenburg
The County of Isenburg was a region of Germany located in southern present-day Hesse, located in territories north and south of Frankfurt. The states of Isenburg emerged from the Niederlahngau (located in the Rhineland-Palatinate), which partitioned in 1137 into Isenburg-Isenburg and Isenburg-Limburg-Covern. These countships were partitioned between themselves many times over the next 700 years.18700
Sam Adams (footballer, born 1989)
Sam Adams (born 2 October 1989) is a Ghanaian professional footballer who plays as a midfielder for Ghanaian Premier League side Aduana Stars. Adams won the Ghana Premier League in 2017 and the Ghana Super Cup in 2018 during his first stint with Aduana Stars. He joined Asante Kotoko in December 2019 but left after 8 months after his contract was terminated only to rejoin Aduana Stars in 2020.

Ghana Premier League
The Ghana Premier League is the top professional association football league in Ghana organized by the Ghana Football Association and formed in 1958 to replace a previous league incarnation, the Gold Coast Club Competition which ran from 1933 to 1953–54. As of the first quarter of 2024, the league was ranked as the 8th best league in Africa by TeamForm.com.

Asante Kotoko is the most successful team in the league with 25 titles, followed by Accra Hearts of Oak with 20. The bottom 3 teams are relegated at the end of each season and placed in each zone of the Ghanaian Division One League.

The 2019–20 season was halted and eventually cancelled due to the COVID-19 pandemic in Ghana that mirrored the cause of postponement or cancellation of association football leagues and competitions across the globe.
Brad Hill (baseball)
Brad L. Hill (born May 2, 1962) is an American baseball coach and former player, who is the head baseball coach of the Emporia State Hornets. He played college baseball at Emporia State from 1982 to 1985. He then served as the head coach of the Hutchinson Blue Dragons (1988–1990), Central Missouri State Mules (1995–2003) and the  Kansas State Wildcats (2004–2018). Under him, the Wildcats have appeared in six consecutive Big 12 baseball tournaments (2007–2012). His teams have also qualified for three NCAA Division I Baseball Championships. Hill was the coach at Central Missouri State from 1995 to 2003. He won a Division II National Championship there in 2003, and was National Runner-up in 2001.

NCAA Division I baseball tournament
The NCAA Division I Baseball Championship is held each year from May through June and features 64 college baseball teams in the United States, culminating in the eight-team Men's College World Series (MCWS) at Charles Schwab Field Omaha in Omaha, Nebraska.

The tournament is unique in that it features four tiers of competition, alternating between double-elimination brackets and best-of-three series. In fact, throughout the entire 64-team tournament, a team can lose a total of four games and still be crowned champions.
Radnor, Pennsylvania
Radnor is a community which straddles Montgomery and Delaware Counties, Pennsylvania, United States. It is located approximately 13 miles west of Philadelphia, in the Main Line suburbs. The community was named after Radnor, in Wales.

Radnor is home to Cabrini University and a large office complex by the train station. The southern portion, by Lancaster Avenue, was rapidly commercialized in the 1980s, and it is currently one of suburban Philadelphia's premier office destinations.

Cabrini University
Cabrini University was a private Catholic university in Radnor Township, Pennsylvania. It was founded by the Missionary Sisters of the Sacred Heart of Jesus in 1957, and was named after the first American naturalized citizen saint, Mother Frances Cabrini. It was one of the first universities in the United States to make community service a graduation requirement for all undergraduates; having a core curriculum centered on social justice. Due to ongoing financial challenges, the university closed at the end of the 2023–2024 academic year, with ownership of the university's campus passing to Villanova University.
Utah State Route 108
State Route 108 (SR-108) is a state highway in the U.S. state of Utah that spans 12.920 miles (20.793 km) in Davis and Weber Counties. The road connects I-15 and Layton to Syracuse and Clinton before terminating at SR-126 in Roy. The entire route is within the Ogden-Clearfield metropolitan area.

Davis County, Utah
Davis County is a county in northern Utah, United States. As of the 2020 United States census, the population was 362,679, making it Utah's third-most populous county. Its county seat is Farmington, and its largest city by both population and area is Layton.

Davis County is part of the Ogden-Clearfield, UT Metropolitan Statistical Area as well as the Salt Lake City-Provo-Orem, UT Combined Statistical Area.
Nelson Senkatuka
Nelson Senkatuka (born 10 September 1997) is a Ugandan professional footballer who plays as a striker for Bright Stars FC and the Uganda national team.

Senkatuka begun his career at Hope Doves FC in Kampala where he spent two seasons and played for  Erith and Belvedere F.C., Cranes United FC, Kampala City Council,  Proline Football Club and currently in Bright Stars FC.

Bright Stars FC
Bright Stars Football Club, also Soltilo Bright Stars, is a professional football club. They play in the top division of Ugandan football, the Ugandan Super League.

In September 2017, it was announced that Japan International Keisuke Honda, through his management company called Honda Estilo, bought a controlling interest in the club. Their motto is "Always Innovating, Never Imitating."
Andy Adler
Andy Adler (born August 19, 1986) is a bilingual sportscaster, journalist, and television personality who serves as evening sports anchor at CBS 11 (KTVT) and co-host of the Dallas Cowboys Pre- and Post-game shows for CBS. Adler was previously at WPIX in New York and served as lead sports anchor and sports director, as well as host of the New York Yankees pre-game shows. She was previously a co-anchor of KNBC's Today in LA weekend edition and co-host of the Los Angeles Lakers pre-game, halftime, and post-game shows on Time Warner Cable SportsNet LA. Prior to that, she was a sports anchor for Fox in New York, WNYW. Adler is known as the first female sports director in a top market and the Emmy nominated interview segment, 'One on One with Andy Adler,' in collaboration with Sports Illustrated.

WPIX
WPIX (channel 11), branded PIX 11, is a television station in New York City, serving as the de facto flagship of The CW. The station is owned by Mission Broadcasting and operated under a local marketing agreement (LMA) by Nexstar Media Group, which owns 77.1% of the network. Since its inception in 1948, WPIX has maintained studios and offices in the Daily News Building on East 42nd Street (also known as "11 WPIX Plaza") in Midtown Manhattan. The station's transmitter is located at the Empire State Building.

WPIX is also available as a regional superstation via satellite and cable in the United States and Canada. It is the largest Nexstar-operated station by population of market size.
Tacoma Stars
The Tacoma Stars are an American professional indoor soccer team based in Tacoma, Washington, that competes in the Major Arena Soccer League (MASL). The franchise also operates in USL League Two, a minor outdoor league. Founded in 2003, the indoor team plays its home games at ShoWare Center in Kent, Washington. First playing in 2024, the outdoor men's team and outdoor women's team, the Tacoma Galaxy, play home games at Bellarmine Preparatory School in Tacoma.

The club also fields an indoor women's side under the Tacoma Galaxy name. The club fields two reserve teams both with the name Tacoma Stars Reserves, in the indoor WISL junior league, and the outdoor youth Cascadia Premier League.

Major Arena Soccer League
The Major Arena Soccer League (MASL) is a professional indoor soccer league in North America. The MASL features teams playing coast-to-coast in the United States and Mexico. The league is the highest level of arena soccer in North America. The league draws talent from a global talent pool with players from Major League Soccer (MLS), Liga MX, and many national teams. With a new management team, the league has grown in popularity and commercially. Former USMNT and MLS star Landon Donovan played in the MASL, as do multiple international players.
Rob Rensenbrink
Pieter Robert Rensenbrink (Dutch pronunciation: [ˈrɔp ˈrɛnsə(m)ˌbrɪŋk]; 3 July 1947 – 24 January 2020) was a Dutch footballer and member of the Netherlands national team that reached two FIFA World Cup finals, in 1974 and 1978. A creative and prolific left winger or forward, he became a legend in Belgium while playing in the great Anderlecht side of the 1970s. He is the UEFA Cup Winners' Cup's all-time top scorer, with 25 goals. A talented dribbler as well as a cool finisher and adequate passer, he only ever missed two penalties in his entire career. He was also the first winner of the Onze d'Or in 1976.

Onze d'Or
The Onze d'Or (alternative name: Onze Mondial European Footballer of the Year) is an association football award given by French magazine Onze Mondial since 1976. The award honors the best player in Europe, with any player in a European league eligible. Since 1991, there has also been a vote for the best coach of the year.

Onze Mondial's readers select their ideal team of the season, Onze de Onze ("Onze's eleven"), and among those players they choose the top three, who receive the Onze d'Or ("Golden Onze"), Onze d'Argent ("Silver Onze"), and Onze de Bronze ("Bronze Onze"), respectively. The awards were based on the previous calendar year until 2009, but moved to a seasonal format beginning with the 2010–11 season.

Lionel Messi is the only player to have won the award on four occasions (2009–2012, 2018). Only two other players have won the Onze d'Or three times: Michel Platini (1983–1985) and Zinedine Zidane (1998, 2000–2001).
Steve Erickson (sailor)
Steven Richard Erickson (born August 14, 1961) is an American sailor and Olympic champion in the Star class. He competed at the 1984 Summer Olympics in Los Angeles and won a gold medal in the Star together with William Earl Buchan.

Sailing at the 1984 Summer Olympics – Star
The Star was a sailing event on the Sailing at the 1984 Summer Olympics program in Long Beach, Los Angeles County, California. Seven races were scheduled. 38 sailors, on 19 boats, from 19 nations competed.
World Trade Center Abu Dhabi
The World Trade Center Abu Dhabi is a complex of two skyscrapers in Abu Dhabi, United Arab Emirates. Construction of these towers was scheduled to end in 2010, though the 2008 financial crisis pushed the project completion date to 2014. The complex includes two malls, and one Courtyard by Marriott hotel. The complex was initially planned to house three skyscrapers, but the 2008 crisis forced the contractors to withdraw construction of the Hotel Tower, the result being two skyscrapers.

Courtyard by Marriott
Courtyard by Marriott is an American brand of hotels owned by Marriott International. The hotels are primarily targeted to business travelers (but also accommodate traveling families). As of June 30, 2020, there were 1,254 Courtyard Marriott Hotels worldwide with 187,095 rooms in addition to 288 hotels with 49,335 rooms in the pipeline.
Football in Åland
Football in Åland is governed by the Åland Football Association (ÅFF), which was founded in 1943. ÅFF is a member of Football Association of Finland.

Åland has 11 football clubs across different levels, ages, and genders. Åland even has its own national teams, Åland official football team and Åland women's official football team, despite not being a fully sovereign state or having membership to UEFA or FIFA. Åland women's team won the 2011 Island Games women's football tournament on the Isle of Wight.

Football clubs of Åland play in leagues and competitions of Finland and Sweden. As of 2025, IFK Mariehamn plays in the Finnish men's premier league Veikkausliiga and Åland United plays in the Finnish women's top division Kansallainen Liiga.

Åland United
Åland United is a Finnish women's football club based in Lemland, Åland. They compete in the Kansallinen Liiga, the premier women's football league in Finland.

In 2004 Åland's clubs Lemlands IF and IF Finströms Kamraterna decided to strengthen the women's football in the region. Their combined team operated under Lemlands IF using the name Åland United. United managed promotion to the top national women's league, the Naisten Liiga, in 2005. In 2008 other Ålandic clubs Sunds IF, IFK Mariehamn and Saltviks IF joined in the cooperation and Åland United became an independent, pure women's football club.

In 2009 Åland United won the championship and played in the 2010–11 UEFA Women's Champions League. They started in the round of 32 and lost both legs to reigning champion Turbine Potsdam. In subsequent seasons Åland United has been 3rd (2010), 4th (2011), 2nd (2012) and champions (2013)
Asterix and the Magic Carpet
Asterix and the Magic Carpet is the twenty-eighth volume of the Asterix comic book series by René Goscinny (stories) and Albert Uderzo (illustrations). It was first published in 1987, and was translated into English in 1988.  It is the fourth Asterix album to be published after the death of René Goscinny in 1977 and is thus both written and drawn by Albert Uderzo alone.

The full original French title was Astérix chez Rahàzade ou Le compte des mille et une heures (Asterix meets Orinjade or the 1001 Hours Countdown), a reference to Queen Scheherazade who tells the famous 1001 Nights collection of stories.

Asterix and Son
Asterix and Son (French: Le Fils d'Astérix, "Asterix's Son") is the twenty-seventh volume of the Asterix comic book series, created by author René Goscinny and illustrator Albert Uderzo.  It was the third Asterix album to be written and illustrated by Uderzo.
Tongan language
Tongan (English pronunciation: /ˈtɒŋ(ɡ)ən/ TONG-(g)ən; lea fakatonga) is an Austronesian language of the Polynesian branch native to the island nation of Tonga. It has around 187,000 speakers. It uses the word order verb–subject–object and, although primarily spoken, the written form uses Latin script.

ʻOkina
The ʻokina (Hawaiian pronunciation: [ʔoˈkinɐ]) is the letter that transcribes the glottal stop consonant in Hawaiian. It does not have distinct uppercase and lowercase forms, and is represented electronically by the modifier letter turned comma: ʻ.

A phonemic glottal stop exists in many other Polynesian languages as well; these are usually written by a similar apostrophe-like letter.
Makai Mason
Makai Mason (born May 4, 1995) is an American-German professional basketball player who last played for Baxi Manresa of the Liga ACB. He played college basketball for the Yale Bulldogs and Baylor Bears.

Bàsquet Manresa
Club Bàsquet Manresa S.A.D., also known as Baxi Manresa for sponsorship reasons, is a professional basketball club based in Manresa, Spain. The team plays in the Liga ACB and the EuroCup Basketball. It home arena is the Pavelló Nou Congost. In 1998, Bàsquet Manresa won the Spanish Championship in one of the most astonishing and well-known sporting accomplishment in Europe.

Joan "Chichi" Creus is the team's most decorated player; he was the Spanish Cup Most Valuable Player in 1996, and the ACB Finals MVP two years later. Some others well known players that had played for Bàsquet Manresa are Juan Domingo de la Cruz, Roger Esteller, Derrick Alston, Serge Ibaka, Andrés Nocioni, Rolando Frazer, and the Basketball Hall of Famer George Gervin, that at the age of 38 spent one year in the team, averaging 23.1 points and helping them to avoid the relegation from the Spanish top division.
Barriers to entry
In theories of competition in economics, a barrier to entry, or an economic barrier to entry, is a fixed cost that must be incurred by a new entrant, regardless of production or sales activities, into a market that incumbents do not have or have not had to incur.
Because barriers to entry protect incumbent firms and restrict competition in a market, they can contribute to distortionary prices and are therefore most important when discussing antitrust policy. Barriers to entry often cause or aid the existence of monopolies and oligopolies, or give companies market power.
Barriers of entry also have an importance in industries. First of all it is important to identify that some exist naturally, such as brand loyalty.
Governments can also create barriers to entry to meet consumer protection laws, protecting the public. In other cases it can also be due to inherent scarcity of public resources needed to enter a market.

Brand loyalty
In marketing and consumer behaviour, brand loyalty refers to a consumer’s consistent preference for a particular brand and their commitment to repeatedly purchasing its products or services despite competing alternatives, market changes, or product shortcomings. It may also be reflected in behaviors such as positive word-of-mouth advocacy.

Corporate brand loyalty describes a pattern in which consumers repeatedly purchase products from the same manufacturer rather than switching to competitors. In business-to-business contexts, a similar concept is sometimes referred to as source loyalty.

Brand loyalty implies an attitudinal commitment and should be distinguished from habitual purchasing, which may occur without emotional attachment or deliberate preference.

Organizations whose financial performance and ethical positioning rely significantly on maintaining strong customer loyalty are sometimes described as operating under a loyalty-driven business model.