hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Fermat's factorization method
Fermat's factorization method, named after Pierre de Fermat, is based on the representation of an odd integer as the difference of two squares:

That difference is algebraically factorable as ; if neither factor equals one, it is a proper factorization of N.

Each odd number has such a representation. Indeed, if  is a factorization of N, then

Since N is odd, then c and d are also odd, so those halves are integers. (A multiple of four is also a difference of squares: let c and d be even.)

In its simplest form, Fermat's method might be even slower than trial division (worst case). Nonetheless, the combination of trial division and Fermat's is more effective than either by itself.

Pierre de Fermat
Pierre de Fermat (/fɜːrˈmɑː/; French: [pjɛʁ də fɛʁma]; 17 August 1601 – 12 January 1665) was a French magistrate, polymath, and above all mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of differential calculus, then unknown, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics. He is best known for his Fermat's principle for light propagation and his Fermat's Last Theorem in number theory, which he described in a note at the margin of a copy of Diophantus' Arithmetica. He was also a lawyer at the parlement of Toulouse, France, a poet, a skilled Latinist, and a Hellenist.
Sibley and Holmwood Candy Factory and Witkop and Holmes Headquarters
Sibley and Holmwood Candy Factory and Witkop and Holmes Headquarters, also known as the Weed & Company Building, are two connected historic commercial buildings located in downtown Buffalo, Erie County, New York, United States. The Sibley & Holmwood Candy Factory (149 Swan Street) was built in 1896 and is a five-story, nine-bay-wide brick commercial block with late-Gothic detailing. It features Gothic window arches, decorative cast-iron columns on the storefront, and corbelled cornice. The Witkop & Holmes Headquarters (145 Swan Street) was designed by the architectural firm Bethune, Bethune & Fuchs and built in 1901.  It is a four-story, three-bay-wide brick commercial block. Both buildings have flat roofs. The building has been renovated to house loft apartments.

It was listed on the National Register of Historic Places in 2014.

Louise Blanchard Bethune
Louise Blanchard Bethune (July 21, 1856 – December 18, 1913) was the first American woman known to have worked as a professional architect. She was born in Waterloo, New York. Blanchard worked primarily in Buffalo, New York with her husband at Bethune, Bethune & Fuchs.

Her largest project was the Hotel Lafayette, including its expansion project, but she also worked on many other residential and commercial projects, including many public school buildings. The Buffalo Meter Company Building was renamed Bethune Hall in her honor by the University at Buffalo.
Korey Lovett
Korey Lovett (born 27 April 1996) is an American tennis player.

Lovett has a career high ATP singles ranking of 1,618 achieved on 1 October 2018 and a doubles ranking of No. 308 achieved on 24 February 2020.

Lovett made his ATP main draw debut at the 2014 BB&T Atlanta Open in the doubles draw partnering Becker O'Shaughnessey. Lovett also played college tennis at the University of Central Florida.

2014 BB&T Atlanta Open
The 2014 BB&T Atlanta Open was a professional tennis tournament played on hard courts. It was the 27th edition of the tournament, and part of the 2014 ATP World Tour. It took place at Atlantic Station in Atlanta, United States between 19 and 27 July 2014. It was the first men's event of the 2014 US Open Series.
No Frills (TV series)
No Frills is a television sitcom broadcast on BBC1 in 1988, and consisted of 7 episodes. It starred Kathy Staff as Molly Bickerstaff, a recently widowed woman who moves from Oldham to live in London with her divorced daughter Kate (Belinda Sinclair) and goth granddaughter Suzy (Katharine Schlesinger).

Katharine Schlesinger
Katharine Schlesinger (born 29 April 1963) is a British actress. In 1987, she starred as Catherine Morland in the BBC Television  adaptation of Jane Austen's Northanger Abbey and Anne Frank in the BBC's The Diary of Anne Frank. She is the niece of the film director John Schlesinger and the great-niece of Dame Peggy Ashcroft.
Radusz, West Pomeranian Voivodeship
Radusz [ˈraduʂ] (formerly German bef. 1939 Altmühl bei Grünwalde, 1939 Burghof) is a village in the administrative district of Gmina Grzmiąca, within Szczecinek County, West Pomeranian Voivodeship, in north-western Poland.

For the history of the region, see History of Pomerania.

The village has a population of 80.

Gmina Grzmiąca
Gmina Grzmiąca is a rural gmina (administrative district) in Szczecinek County, West Pomeranian Voivodeship, in north-western Poland. Its seat is the village of Grzmiąca, which lies approximately 23 kilometres (14 mi) north-west of Szczecinek and 129 km (80 mi) east of the regional capital Szczecin.

The gmina covers an area of 204.49 square kilometres (79.0 sq mi), and as of 2006 its total population is 5,012.

Gmina Grzmiąca is bordered by the gminas of Barwice, Bobolice, Borne Sulinowo, Szczecinek and Tychowo.
Devendra Banhart
Devendra Obi Banhart (born May 30, 1981) is an American singer-songwriter and visual artist. He was born in Texas and grew up in Venezuela and California. In 2000, he dropped out of the San Francisco Art Institute in San Francisco to pursue a musical career. In 2002, Banhart released his debut album and he is best known for his albums in the late 2000s such as Cripple Crow and Smokey Rolls Down Thunder Canyon. He has since expanded his career to incorporate his interest and training in the visual arts.

San Francisco Art Institute
San Francisco Art Institute (SFAI) was a private college of contemporary art in San Francisco, California. Founded in 1871, SFAI was one of the oldest art schools in the United States and the oldest west of the Mississippi River. Approximately 220 undergraduates and 112 graduate students were enrolled in 2021. The institution was accredited by the Western Association of Schools and Colleges (WASC) and the National Association of Schools of Art and Design (NASAD), and was a member of the Association of Independent Colleges of Art and Design (AICAD). The school closed permanently in July 2022.
Cornucopia, Wisconsin
Cornucopia is an unincorporated census-designated place in the town of Bell in northern Bayfield County, Wisconsin, United States. It is situated on Lake Superior at the northern end of the Bayfield Peninsula. It is along Wisconsin Highway 13 and County Highway C. As of the 2020 census, its population was 103, an increase over the figure of 98 tabulated in 2010. The community borders the lake at Siskiwit Bay, between Roman's Point and Mawikwe (formerly Squaw) Point. It is near a mainland portion of the Apostle Islands National Lakeshore, which features the Mawikwe Bay Sea Caves.

Most residents of the Town of Bell with Cornucopia mailing addresses are considered residents of Cornucopia.

Apostle Islands National Lakeshore
The Apostle Islands National Lakeshore is a U.S. national lakeshore consisting of 21 islands (Apostle Islands) and shoreline encompassing 69,540 acres (28,140 ha) on the northern tip of Wisconsin on the shore of Lake Superior.
It is known for its collection of historic lighthouses, sandstone sea caves, a few old-growth remnant forests, and natural animal habitats. It is featured on the America the Beautiful Quarters series.

The Apostle Islands National Lakeshore is located in Bayfield, Wisconsin, on Lake Superior, the "largest, cleanest, and coldest of the Great Lakes". The lakeshore comprises beaches, cliffs, water, and 21 islands. Of its area, 42,308 acres is land and 27,232 acres is water, extending 1/4 mile from the 155 miles of shoreline. Madeline Island, with commercial establishments of the town of La Pointe, is the only one of the Apostle Islands not included in the national lakeshore, although a portion of the island is protected as Big Bay State Park.
Nova Scotia Route 348
Route 348 is a collector road in the Canadian province of Nova Scotia.

It is located in the northeastern part of the province and connects Little Harbour at Route 289 with Melrose at Trunk 7.

In the town of Trenton it runs on "North Main Street," "Main Street" and "Trenton Road."  In the neighbouring town of New Glasgow it runs on "North Provost Street," "Provost Street" and "Jury Street" (southbound), "Archimedes Street" (northbound), and the "East River Road."

New Glasgow, Nova Scotia
New Glasgow is a town in Pictou County, in the province of Nova Scotia, Canada. It is situated on the banks of the East River of Pictou, which flows into Pictou Harbour, a sub-basin of the Northumberland Strait.

The town's population was 9,471 in the 2021 census. New Glasgow is at the centre of the province's fourth largest urban area; the population of the New Glasgow census agglomeration in the 2021 census was 34,397. The New Glasgow census agglomeration includes the smaller adjacent towns of Stellarton, Westville, and Trenton as well as adjacent rural areas of the county.
Statue of Billy Graham
A bronze statue of American evangelist Billy Graham is installed at the United States Capitol's crypt, in Washington, D.C., as part of the National Statuary Hall Collection. It was designed by artist Chas Fagan.

Unveiled in May 2024, the sculpture was gifted by the U.S. state of North Carolina, replacing the statue of Charles Brantley Aycock.

United States Capitol crypt
The United States Capitol crypt is the large circular room filled with forty neoclassical Doric columns directly beneath the United States Capitol rotunda. It was built originally to support the rotunda as well as offer an entrance to Washington's Tomb. It currently serves as a museum and a repository for thirteen statues of the National Statuary Hall Collection.
2001 Florida's 1st congressional district special election
The 2001 special election for Florida's 1st congressional district took place on October 16, 2001, to fill the vacancy caused by Representative Joe Scarborough's resignation. Florida's 1st congressional district was a staunchly conservative district stretching from Panama City Beach to Pensacola in the Florida Panhandle.

State Representative Jeff Miller, the Republican nominee, easily defeated Steve Briese, a financial writer and the Democratic nominee.

Joe Scarborough
Charles Joseph Scarborough (/ˈskɑːrbʌroʊ/; born April 9, 1963) is an American television host and former politician who is the co-host of Morning Joe on MS NOW with his wife Mika Brzezinski and Willie Geist. He previously hosted Scarborough Country on the same network. A former member of the Republican Party, Scarborough was in the United States House of Representatives for Florida's 1st district from 1995 to 2001. He was appointed to the President's Council on the 21st Century Workforce in 2002 and was a visiting fellow at the Harvard Institute of Politics at the Harvard Kennedy School of Government. He was named in the 2011 Time 100 as one of the most influential people in the world.
Up (film series)
The Up series of documentary films follows the lives of ten boys and four girls in England, beginning in 1964, when they were seven years old. The first film was titled Seven Up!, with later films adjusting the number in the title to match the age of the subjects at the time of filming. The documentary has had nine episodes—one every seven years—thus spanning 56 years. The series has been produced by Granada Television for ITV, which has broadcast all of them except 42 Up (1998), which was broadcast on BBC One. Individual films and the series as a whole have received numerous accolades; in 1984, the then-latest instalment, 28 Up, was chosen for Roger Ebert's list of the ten greatest films of all time. The series was voted the most influential British TV programme of the past 50 years, in a 2024 poll of the Broadcasting Press Guild.

Charles Furneaux (TV producer)
Charles St John Wallace Furneaux (born 1957) is a British television producer and documentary maker. He began his career as an assistant producer with the BBC, becoming a commissioning editor at Channel 4 in 1994. Furneaux then went to Talkback Thames in 2003 as Head of Specialist Factual and Documentaries resigning in 2007 to manage his own production company, Kaboom Film & TV.
ShadowHawk (character)
ShadowHawk is a superhero created by Jim Valentino for Image Comics.

He was first advertised in the Malibu Sun free promotional magazine in May 1992. His official Image Comics debut was in the second issue of Youngblood series (June 1992), written and illustrated by Rob Liefeld.

Originally, the name ShadowHawk was to be used for the Marvel character Starhawk while he had darkness powers, but Tom DeFalco convinced Valentino to use the name for a new character instead.

Image United
Image United is an incomplete comic book limited series published by Image Comics. The intent of the series was to re-unite the founders of Image Comics on a joint project, serving as a crossover among various Image Universe titles. However, there were delays in production, and only three of the planned six issues were published in November 2009 (plus a spinoff, the prologue-centric #0), with artist Rob Liefeld eventually confirming that no further issues would be forthcoming.
Khouribga
Khouribga (Moroccan Arabic: خريبڭة, romanized: khurībga, [xuriːbɡa]) is the capital of Khouribga Province in the Béni Mellal-Khénifra region, Morocco. With a population of 342,125  (2024 census), Khouribga owes its growth to the phosphate deposits nearby.

Béni Mellal-Khénifra
Béni Mellal-Khénifra (Arabic: بني ملال - خنيفرة, romanized: banī mallāl - ḵunayfira) is one of the twelve regions of Morocco, covering an area of 28,374 km2, and recorded a population of 2,520,776 in the 2014 Moroccan census. The capital of the region is Beni Mellal.
The Anniversary (1968 film)
The Anniversary is a 1968 British black comedy film directed by Roy Ward Baker for Hammer Films and Seven Arts and starring Bette Davis. The screenplay, by Jimmy Sangster, was adapted from Bill MacIlwraith's 1966 play.

Jimmy Sangster
James Henry Kinmel Sangster (2 December 1927 – 19 August 2011) was a Welsh screenwriter and film director, best known for his work on the initial horror films made by Hammer Film Productions, including The Curse of Frankenstein (1957) and Dracula (1958).
The Gray Cloth
The Gray Cloth with Ten Percent White: A Ladies' Novel (in German, Das graue Tuch und zehn Prozent Weiß: Ein Damenroman) is an avant-garde novel by the fantasist and visionary writer Paul Scheerbart, first published in 1914. The book expresses its author's commitment to the use of glass in modern architecture, which had a significant impact on the concepts of German Expressionism.

Paul Scheerbart
Paul Karl Wilhelm Scheerbart (8 January 1863, Danzig – 15 October 1915, Berlin) was a German author of speculative fiction literature and drawings. He was also published under the pseudonym Kuno Küfer and is best known for the book Glasarchitektur (1914).

Scheerbart was associated with expressionist architecture and one of its leading proponents, Bruno Taut. He composed aphoristic poems about glass for Taut's Glass Pavilion at the Werkbund Exhibition (1914).
War of the Worlds: New Millennium
War of the Worlds: New Millennium  is a science fiction novel by Douglas Niles, released in 2005 by Tor Books.

After the most recent uncrewed mission to Mars inexplicably fails, interest in the Red Planet is still high. The whole world watches as a bright spot of light appears daily on the Martian surface. As they continue, theories abound about what is causing it. Telescopes pick up movement in space: something came from Mars and is headed towards Earth.

As explained in the Author's Note  of the novel, H. G. Wells wrote the original 1897 The War of the Worlds prior to any modern military conflict (such as World War I or World War II). This novel is the Martian invasion of Earth in 2005, in effect updating the Martians and the military’s actual and doctrinal responses.

Douglas Niles
Douglas Niles (born December 1, 1954, in Brookfield, Wisconsin) is a fantasy author and game designer. Niles was one of the creators of the Dragonlance world and the author of the first three Forgotten Realms novels, the Star Frontiers space opera setting and the Top Secret S/I espionage role-playing game.
People's Republic of Benin
The People's Republic of Benin (French: République populaire du Bénin; sometimes translated literally as the Benin Popular Republic or Popular Republic of Benin) was a communist state located in the Gulf of Guinea on the African continent, which became present-day Benin in 1990. The People's Republic was established on 30 November 1975, after the 1972 coup d'état in the Republic of Dahomey. It effectively lasted until 1 March 1990, with the adoption of a new constitution, and the abolition of Marxism–Leninism in the nation in 1989.

1972 Dahomeyan coup d'état
The 1972 Dahomeyan coup d'état was a military coup staged on 26 October 1972 by Major (later General) Mathieu Kérékou, who took control of the Republic of Dahomey and ended a system of government established following the annulled 1970 presidential election, in which three members of the Presidential Council (Hubert Maga, Justin Ahomadégbé-Tomêtin and Sourou-Migan Apithy) were to rotate in power. Ahomadégbé-Tomêtin served as the Chairman at the time of the coup.
Revaya
Revaya (Hebrew: רְוָיָה) is a moshav in the Beit She'an Valley in northern Israel. Located about six kilometres south of Beit She'an, near Sde Trumot and west of Israel Highway 90, it falls under the jurisdiction of Valley of Springs Regional Council. In 2022 it had a population of 459.

The moshav is one of four settlements established as a group: Revaya, Sde Trumot, Tel Teomim, and Rehov.

Emek HaMaayanot Regional Council
Emek HaMa'ayanot Regional Council (Hebrew: מועצה אזורית עמק המעיינות, Mo'atza Azorit Emek HaMa'ayanot, lit. Valley of the Springs Regional Council) is a regional council in the Northern District of Israel that encompasses most of the settlements in the Beit She'an Valley. Until 2008 it was known as the Beit She'an Valley Regional Council (Mo'atza Azorit Bik'at Beit She'an).
Francesco Sarego
Francesco Sarego (born August 1, 1939, in Cologna Veneta) was an Italian clergyman and bishop for the Roman Catholic Diocese of Goroka. He was appointed bishop in 1995.

Between 2005 and 2008, he was the President of the Catholic Bishops Conference of Papua New Guinea and Solomon Islands.

Francesco Sarego retired in 2016.

Diocese of Goroka
The Diocese of Goroka is a Latin Catholic suffragan diocese of the Archdiocese of Mount Hagen, based in Goroka. It was erected Vicariate Apostolic in 1959 and elevated to a diocese in 1966. In 1982, part of the diocese was separated to become the Diocese of Kundiawa.
Simon Montacute
Simon Montacute (died 1345) was a medieval Bishop of Worcester and Bishop of Ely.

Montacute was the third son of William Montagu, 2nd Baron Montagu (d. 18 October 1319), by Elizabeth Montfort (d. August 1354), daughter of Sir Piers Montfort of Beaudesert, Warwickshire. He had two elder brothers, John, who died in August 1317, and William Montagu, 1st Earl of Salisbury, and a younger brother, Edward Montagu, 1st Baron Montagu, who married Alice of Norfolk, daughter of Thomas of Brotherton and granddaughter of Edward I. Among his seven sisters were Elizabeth, Prioress of Halliwell, and Maud and Isabel, successively Abbesses of Barking from 1341 to 1358.

Montacute was nominated to the see of Worcester on 11 December 1333 and consecrated on 8 May 1334. and was then translated to the see of Ely on 14 March 1337. As bishop of Ely, he was involved in the foundation of Peterhouse, Cambridge, being largely responsible for an early set of statutes for the college. He died on 20 June 1345.

Holywell Priory
Holywell Priory or Haliwell, Halliwell, or Halywell (various spellings),  was a religious house in Shoreditch, formerly in the historical county of Middlesex and now in the London Borough of Hackney. Its formal name was the Priory of St John the Baptist.

The Priory stood at Holywell Lane on the west side of Shoreditch towards Hoxton, its  precinct lying within the area now bounded by Batemans Row, Shoreditch High Street, Holywell Lane, and Curtain Road.
Balmain Water Polo Club
UTS Balmain Tigers Water Polo Club is an Australian club water polo team that competes in the National Water Polo League.  They have a men's team and a women's team and are based in Balmain, New South Wales.

The club have been sponsored by the University of Technology Sydney since 2009.

Australian Water Polo League
The Australian Water Polo League (formerly known as the Australian National Water Polo League) is the premier Australian domestic water polo competition. The men's league was established in 1990 with the women's league following in 2004. The league is administered by Water Polo Australia, and is contested by eleven clubs, each fielding a women's and a men's team. As of 2024 five clubs are based in Sydney and one each in Melbourne, Adelaide, Brisbane, Fremantle, Newcastle and Perth.

Seasons of the AWL run from January to April and include a 28-round regular season, followed by a finals series playoff involving the six highest-placed teams, which culminates in a grand final match.
Alta Jerarquía
Alta Jerarquía is the sixth studio album by Puerto Rican singer Tito El Bambino, released on November 24, 2014 by On Fire Music. This album contains more urban songs and collaborations due to requests from the artist by the fans through social networks, who wanted the singer returned to the genre with which he became known. The album included the singles "A Que No Te Atreves" (featuring Chencho of the duo Plan B), "Controlando" and "Adicto a Tus Redes" (featuring Nicky Jam).

It debuted at number three on the US Billboard Top Latin Albums chart, selling over 3,000 copies on the first week.

Tito el Bambino
Efraín David Fines Nevares (born October 5, 1981), known professionally as Tito El Bambino, is a Puerto Rican singer and songwriter who rose to fame as part of the duo Héctor & Tito. In 2010, his song "El Amor", written with Joan Ortiz Espada, was awarded Latin Song of the Year by the American Society of Composers, Authors and Publishers (ASCAP). He was awarded Songwriter of the Year at the 2011 ASCAP.
1998 NIRSA National Soccer Championship
The 1998 NIRSA national soccer championship was the 5th NIRSA National Soccer Championships, the annual national championships for United States-based, collegiate club soccer teams organized by NIRSA. It took place at Georgia Southern University in Statesboro, Georgia from Thursday, November 19 to Saturday, November 21, 1998.

BYU Cougars men's soccer
BYU Cougars men's soccer is an American soccer team based in Provo, Utah, United States. The club has won eleven NIRSA national championships, and it is the only university sponsored soccer program to have ever purchased a franchise, competing in the Premier Development League (now known as USL League Two) from 2003 to 2017. It has since returned to club competition with NIRSA, and the team plays its home games at The Stadium at South Field on the campus of Brigham Young University. The team's colors are dark blue and white.