OpenLLM-France/wikimedia huggingface dataset:
# N conjecture

In number theory, the n conjecture is a conjecture stated by Browkin & Brzeziński (1994) as a generalization of the abc conjecture to more than three integers.

## Formulations

Given $n\geq 3$, let $a_{1},a_{2},...,a_{n}\in \mathbb {Z}$ satisfy three conditions:
    (i) $\gcd(a_{1},a_{2},...,a_{n})=1$
    (ii) $a_{1}+a_{2}+...+a_{n}=0$
    (iii) no proper subsum of $a_{1},a_{2},...,a_{n}$ equals $0$
First formulation
The n conjecture states that for every $\varepsilon >0$, there is a constant $C$ depending on $n$ and $\varepsilon$, such that:
   $\operatorname {max} (|a_{1}|,|a_{2}|,...,|a_{n}|)<C_{n,\varepsilon }\operatorname {rad} (|a_{1}|\cdot |a_{2}|\cdot \ldots \cdot |a_{n}|)^{2n-5+\varepsilon }$
where $\operatorname {rad} (m)$ denotes the radical of an integer $m$, defined as the product of the distinct prime factors of $m$.
Second formulation
Define the quality of $a_{1},a_{2},...,a_{n}$ as
    $q(a_{1},a_{2},...,a_{n})={\frac {\log(\operatorname {max} (|a_{1}|,|a_{2}|,...,|a_{n}|))}{\log(\operatorname {rad} (|a_{1}|\cdot |a_{2}|\cdot ...\cdot |a_{n}|))}}$
The n conjecture states that $\limsup q(a_{1},a_{2},...,a_{n})=2n-5$.

## Stronger form

Vojta (1998) proposed a stronger variant of the n conjecture, where setwise coprimeness of $a_{1},a_{2},...,a_{n}$ is replaced by pairwise coprimeness of $a_{1},a_{2},...,a_{n}$.
There are two different formulations of this strong n conjecture.
Given $n\geq 3$, let $a_{1},a_{2},...,a_{n}\in \mathbb {Z}$ satisfy three conditions:
    (i) $a_{1},a_{2},...,a_{n}$ are pairwise coprime
    (ii) $a_{1}+a_{2}+...+a_{n}=0$
    (iii) no proper subsum of $a_{1},a_{2},...,a_{n}$ equals $0$
First formulation
The strong n conjecture states that for every $\varepsilon >0$, there is a constant $C$ depending on $n$ and $\varepsilon$, such that:
   $\operatorname {max} (|a_{1}|,|a_{2}|,...,|a_{n}|)<C_{n,\varepsilon }\operatorname {rad} (|a_{1}|\cdot |a_{2}|\cdot \ldots \cdot |a_{n}|)^{1+\varepsilon }$
Second formulation
Define the quality of $a_{1},a_{2},...,a_{n}$ as
    $q(a_{1},a_{2},...,a_{n})={\frac {\log(\operatorname {max} (|a_{1}|,|a_{2}|,...,|a_{n}|))}{\log(\operatorname {rad} (|a_{1}|\cdot |a_{2}|\cdot ...\cdot |a_{n}|))}}$
The strong n conjecture states that $\limsup q(a_{1},a_{2},...,a_{n})=1$.
# Netherlands at the 1984 Winter Paralympics

Netherlands competed at the 1984 Winter Paralympics in Innsbruck, Austria. The team included six athletes, five men and one woman. Competitors from Netherlands won 0 medals to finish 15th in the medal table.

## Medalists

No medals are won during these Paralympic games.

## Alpine skiing

* Wiel Bouten
* Karel Hanse

## Cross-country skiing

* Tineke Hekman
* Jan Visser

## Ice Sledge Speed Racing

* Willem Hofma
* Henk de Jong
# Dipodomyinae

Dipodomyinae is a subfamily of heteromyid rodents, the kangaroo rats and mice. Dipodomyines, as implied by both their common and scientific names, are bipedal; they also jump exceptionally well. Kangaroo rats and mice are native to desert and semidesert ecosystems of western North America from southern Canada to central Mexico. They are generally herbivorous foragers, and dig and live in burrows.

## Taxonomy

Dipodomyinae is the sister group of a Perognathinae-Heteromyinae clade; the two are estimated to have split about 22-24 million years (Ma) ago. The most recent common ancestor of extant dipodomyines is thought to have lived 15-16 Ma ago, when the two genera split. The most recent common ancestors of extant members of Dipodomys and Microdipodops are thought to have lived 10-11 and 7-8 Ma ago, respectively.
* Subfamily Dipodomyinae
** Genus Dipodomys — kangaroo rats
*** Agile kangaroo rat, Dipodomys agilis
*** California kangaroo rat, Dipodomys californicus
*** Gulf Coast kangaroo rat, Dipodomys compactus
*** Desert kangaroo rat, Dipodomys deserti
*** Texas kangaroo rat, Dipodomys elator
*** Big-eared kangaroo rat, Dipodomys elephantinus
*** San Quintin kangaroo rat, Dipodomys gravipes
*** Heermann's kangaroo rat, Dipodomys heermanni
*** Giant kangaroo rat, Dipodomys ingens
*** Merriam's kangaroo rat, Dipodomys merriami
*** Chisel-toothed kangaroo rat, Dipodomys microps
*** Nelson's kangaroo rat, Dipodomys nelsoni
*** Fresno kangaroo rat, Dipodomys nitratoides
*** Ord's kangaroo rat, Dipodomys ordii
*** Panamint kangaroo rat, Dipodomys panamintinus
*** Phillips's kangaroo rat, Dipodomys phillipsii
*** Dulzura kangaroo rat, Dipodomys simulans
*** Banner-tailed kangaroo rat, Dipodomys spectabilis
*** Stephens's kangaroo rat, Dipodomys stephensi
*** Narrow-faced kangaroo rat, Dipodomys venustus
** Genus Microdipodops — kangaroo mice
*** Pale kangaroo mouse, Microdipodops pallidus
*** Dark kangaroo mouse, Microdipodops megacephalus
# La Surprise de l'amour

La Surprise de l'amour is a three-act romantic comedy by French playwright Marivaux. Its title is usually translated into English as The Surprise of Love. La Surprise de l'amour was first performed 3 May 1722 by the Comédie Italienne at the Hotel de Bourgogne in Paris. In this play, a man and a woman who've sworn off love are tricked by their servants into falling in love with each other.
Like many of Marivaux's other comedies, La Surprise de l'amour makes use of stock characters from the Commedia dell'arte. In this play, Arlequin and Columbine are featured.
Théophile Gautier considered this to be Marivaux's finest work.

## Plot summary

After having been betrayed by a woman, Lélio renounces love and retires to the countryside with his valet, Arlequin, whose adventures in love are similar. Arlequin, who loves everything about women, including their faults, struggles with the task of forgetting them. One of Lélio's servants, Jacqueline, hopes to marry Pierre, a servant at the nearby home of the countess. Lélio refuses to allow the two to marry, as he imposes his own viewpoint on his entire household.
The countess, who herself refuses to love men, comes to intervene. Despite the fact that Lélio and the countess swear not to fall in love, a friend of Lélio predicts that this will come to pass. The countess decides to avoid Lélio, but in doing so, she earns his respect and sets in motion the ideas of her servant Columbine. Through the machinations of Columbine and Arlequin (who in turn fall in love themselves), the countess and Lélio ultimately end up together. The play ends with three happy couples: Lélio and the countess, Arlequin and Columbine, and Pierre and Jacqueline.

## Characters

* The countess - a wealthy widow who has sworn off men
* Lélio - a man who has sworn off women
* The baron - a friend of Lélio
* Arlequin - Lélio's valet
* Columbine - The countess' confidente
* Jacqueline - a female servant in Lélio's household
* Pierre - the countess' gardener
# Wang Prachan

Wang Prachan (Thai: วังประจัน, pronounced) is a sub-district (tambon) of Khuan Don District, Satun Province of Thailand, at the boundary to Malaysia.
Thai Hwy 4181, which passes through the sub-district, connects Satun with Wang Kelian in Malaysia.
As of 2007, the sub-district has a population of 2,380.

## Administration

The sub-district is led by a tambon administrative organization (TAO), which was established in 2004. The sub-district itself was established in 1914, and is divided into four villages (muban).
| 1. | Thung Maprang | ทุ่งมะปรัง |
| 2. | Khao Nui | เขานุ้ย |
| 3. | Wang Prachan | วังประจัน |
| 4. | Wang Prachan Tai | วังประจันใต้ |

## Pictures

* Wang Prachan checkpoint seen from Malaysian territory.
* Morning market at Wang Prachan, just before the border crossing into Malaysia.
# Ivanovka, Polevskoy Selsoviet, Kursky District, Kursk Oblast

Ivanovka (Russian: Ивановка) is a rural locality (a khutor) in Polevskoy Selsoviet Rural Settlement, Kursky District, Kursk Oblast, Russia. Population: 2 (2010 Census); 1 (2002 Census);

## Geography

The khutor is located 110 km from the Russia–Ukraine border, 32 km south-east of the district center – the town Kursk, 11 km from the selsoviet center – Polevaya.

### Climate

Ivanovka has a warm-summer humid continental climate (Dfb in the Köppen climate classification).

## Transport

Ivanovka is located 2.5 km from the federal route P-298 (Kursk – Voronezh – P-22 "Kaspy" Highway; a part of the European route E38), 10 km from the nearest railway halt Gutorovo (railway line Klyukva — Belgorod).
The rural locality is situated 29 km from Kursk Vostochny Airport, 112 km from Belgorod International Airport and 178 km from Voronezh Peter the Great Airport.
# Tazeh Kand-e Hajji Khan

Tazeh Kand-e Hajji Khan (Persian: تازه كندحاجي خان, also Romanized as Tāzeh Kand-e Ḩājjī Khān; also known as Tāzeh Kand) is a village in Shaban Rural District, in the Central District of Meshgin Shahr County, Ardabil Province, Iran. At the 2006 census, its population was 33, in 7 families.
# Río de Oro, Cesar

Río de Oro (English: River of Gold) is a town and municipality in the Colombian Department of Cesar.
# Nemazja

Nemazja (Persian: نمازجا, also Romanized as Nemāzjā) is a village in Garmsar Rural District, Jebalbarez-e Jonubi District, Anbarabad County, Kerman Province, Iran. At the 2006 census, its population was 131, in 26 families.
# Hasilpur railway station

Hasilpur Railway Station (Urdu: حاصل پور ریلوے اسٹیشن, Punjabi: حاصل پور ریلوے اسٹیشن) is located in Pakistan.
# Belarus Governorate

Belarus Governorate was an administrative-territorial unit (guberniya) of the Russian Empire established on December 12, 1796. It included the lands acquired after the Second Partition of Poland.
It was dissolved on February 27, 1802, after an administrative reform, split into Vitebsk Governorate and Mogilev Governorate.
# Timothy Butler (sculptor)

Timothy Butler (1806–1885) was a 19th-century British figurative sculptor.
His most noteworthy public works are the dolphin lamps lining the Thames Embankment which date from 1870 and were the first lights to be electrified (1878).

## Life

He was born in Caversham in Oxfordshire in 1806. He won a silver medal at the Society of Arts in 1824. He entered the Royal Academy Schools in 1825 at the recommendation of William Behnes. He won the Royal Academy's silver medal in 1827.
He exhibited at the Royal Academy from 1828 until 1879.
Around 1850 he tutored John Adams-Acton.
From 1851 he lived at 1 Middlesex Place in London. From 1860 he lived at Marylebone Road.
He died at 186 Euston Road near St Pancras in London on 6 September 1885

## Family

His daughter Clehorow Caroline Butler was also a sculptor.

## Works

* Bust of Thomas Musgrave, Bishop of Hereford (1839) exhibited at Royal Academy
* Bust of Sir John Kirby Hedges (1841) currently in wallingford at town council offices
* Bust of the Earl of Granard (1841) exhibited at Royal Academy
* Bust of Sir James Eyre (1842) for Corporation of Hereford
* Bust of Charles Kemble (1844) exhibited at Royal Academy
* Bust of the Hon Mrs Norton (1844) for Richard Brinsley Sheridan
* Bust of Dr Woolff (1846) exhibited at Royal Academy
* Bust of Samuel Cooper (1851) at Royal College of Surgeons
* Statue of the Earl of Leicester (1858) on Dereham Town Hall
* Bust of Joseph Bazalgette (1860) exhibited at Royal Academy
* Bust of Sir Richard Kirby (1862) exhibited at Royal Academy
* Statue of Prof John Narrien at Staff College Farnborough
* Busts of Thomas Eton and his wife (1865) Bristol General Hospital
* Bust of Dr William Clark (1866) Trinity College, Cambridge
* Bust of Lord Rollo (1867) exhibited at Royal Academy
* Bust of Charles Henry Cooper (1868) Cambridge Town Hall
* Lion Heads capping sewage work outlets at South Bank Embankment (1870)
* Ornate lamps on Embankment (1870)
* Bust of Arthur Purvis (1870) Cocanada in Madras
* Statue of Richard Cobden (1877) at Bradford Town Hall
* Bust of T. Hughes (1878) exhibited at Royal Academy
* Bust of Hugh Falconer at Royal Society of London
* Bust of Charles Kahn
* Bust of Prof Edward Turner
* Bust of Edward R. Daniell

## Graves

* James Ince at Hadley in Hertfordshire (1829)
* Anne Marriott at Horsmonden in Kent (1831)
* Lady Thompson at Fareham in Hampshire (1833)
* William Prescott at Hendon (1836)
* Lord Douglas Hallyburton in Kensal Green Cemetery (1841)
* James Ince Jr at Hadley (1845)
* Edward Miller at Goudhurst in Kent (1846)
* John Jackson pugilist (1849) in Brompton Cemetery
* Charles Ince at Hadley (1850)
* General Peter de la Motte in Kensal Green Cemetery (1861)
# Nowruzabad, Zanjan

Nowruzabad (Persian: نوروزاباد, also Romanized as Nowrūzābād) is a village in Chaypareh-ye Pain Rural District, Zanjanrud District, Zanjan County, Zanjan Province, Iran. At the 2006 census, its population was 72, in 16 families.
# Dimerosaccus

Dimerosaccus is a genus of trematodes in the family Opecoelidae. It consists of only one species, Dimerosaccus oncorhynchi. It has been synonymised with Allocreadium oncorhynchi Eguchi, 1931, Plagioporus honshuensis Moravec & Nagasawa, 1998, and P. oncorhynchi (Eguchi, 1931) Peters, 1957.
# Lost Village

Lost Village(s) or The Lost Village may refer to:

## Places

* Abandoned villages
* Deserted medieval villages
* Lost Villages, a group of ten villages in Ontario, Canada

## Entertainment

* Lost Village Festival, a festival in Norton Disney, Lincolnshire, England, UK
* The Lost Village (film), a 1947 French drama film
* The Lost Village (TV series) (Japanese: 迷家-マヨイガ, romanized: Mayoiga), a 2017 Japanese anime
* The Lost Village (video game) (Chinese: 山门与幻境; pinyin: Shānmén yǔ Huànjìng; lit. 'Mountain Gate and Fantasy'), a 2024 Chinese video game
* Smurfs: The Lost Village, a 2017 3D animated U.S. children's film
# Vali Khormayi

Vali Khormayi (Persian: ولي خرمايي, also Romanized as Valī Khormāyī) is a village in Dust Mohammad Rural District, in the Central District of Hirmand County, Sistan and Baluchestan Province, Iran. At the 2006 census, its population was 36, in 6 families.
# Budi Lake

Budi Lake (Spanish: Lago Budi, Spanish:) from the Mapudungun word Füzi which means salt, is a tidal brackish water lake located near the coast of La Araucanía Region, southern Chile. The lake is part of the boundaries between Saavedra and Teodoro Schmidt commune.
Budi Lake is among the few lakes of the west coast of the Americas that have seasonal inflows of sea water. Another difference to many Chilean lakes is that Budi Lake is not of glacial origin and does not lie in the Andes mountain range. Budi Lake is above a coastal plain just south of Nahuelbuta Range and north of the Valdivian Coastal Range where the Chilean Coast Range is very low.
The lake was formed by tectonic movements and eustatic sea level changes.
According to the census of 2002, the zone around the lake is one of the poorest parts of La Araucanía Region, Chile's poorest region in turn. The 13,275 persons who live around the lake form 3,087 families with 30 years as average age. 40% of the population is under 18 years old and 73.2% declare to be Mapuches.
The seashore near the lake was the site of the infamous 1849 wreck of Joven Daniel.
# Komory, Masovian Voivodeship

Komory is a village in the administrative district of Gmina Korytnica, within Węgrów County, Masovian Voivodeship, in east-central Poland. It lies approximately 3 kilometres (2 mi) north-west of Korytnica, 13 km (8 mi) west of Węgrów, and 62 km (39 mi) north-east of Warsaw.
# Oflag VII-A Murnau

Oflag VII-A Murnau was a German Army prisoner-of-war camp for Polish Army officers during World War II. It was located 2 km (1.2 mi) north of the Bavarian town of Murnau am Staffelsee.

## Camp history

The camp was created in September 1939. It consisted of an enclosure 200 m (660 ft) square, surrounded with barbed wire and guard towers. Immediately after the German invasion of Poland, at the beginning of World War II, some 1,000 Polish officers were imprisoned there. On April 27, 1942, additional Polish POWs were transferred there from the so-called "Generals' Camp" Oflag VIII-E in Janské Koupele in German-occupied Czechoslovakia (now in the Czech Republic). After the failed Warsaw Uprising and Operation Tempest more prisoners were brought there from Poland. By early 1945 the number of POWs held in the camp reached over 5,000.
The camps was liberated by troops of the U.S. 12th Armored Division on 29 April 1945.

## List of notable prisoners

Among those imprisoned in Murnau were:

### Rear Admiral (Kontradmirał)

* Józef Unrug

### Divisional Generals (Generał dywizji)

* Władysław Bortnowski
* Tadeusz Kutrzeba
* Tadeusz Piskor
* Juliusz Rómmel

### Brigade Generals (Generał brygady)

* Roman Abraham
* Franciszek Alter
* Władysław Bończa-Uzdowski
* Leopold Cehak [pl]
* Jan Chmurowicz [pl]
* Walerian Czuma
* Franciszek Dindorf-Ankowicz [pl]
* Juliusz Drapella
* Janusz Gąsiorowski
* Edmund Knoll-Kownacki
* Wincenty Kowalski
* Jan Kazimierz Kruszewski [pl]
* Józef Kwaciszewski
* Stanisław Małachowski
* Czesław Młot-Fijałkowski
* Bernard Mond
* Zygmunt Piasecki [pl]
* Wacław Piekarski
* Zygmunt Podhorski
* Emil Przedrzymirski-Krukowicz [pl]
* Zdzisław Przyjałkowski [pl]
* Jan Jagmin-Sadowski
* Antoni Szylling
* Stanisław Taczak
* Wiktor Thommée
* Juliusz Zulauf

### Officers

* Witold Pilecki, former prisoner no 4859 of Auschwitz under assumed name of Tomasz Serafiński; Murnau prisoner no 101892

### Majors

* Seweryn Kulesza
* Edward Pach [pl]

### Captains

* Bronisław Przyłuski [pl]
* Władysław Dawidek [pl]
* Stanisław Guliński [pl]
# Le Petit-Maître corrigé

Le Petit-Maître corrigé is a three-act romantic comedy by French playwright Marivaux. It was first performed on November 6, 1734, by the Comédie-Française in Paris, then located rue des Fossés-Saint-Germain-des-Près.
This play is one of the rare plays of Marivaux not performed by the Comédie Italienne. The first representation was catastrophic, seemingly because Marivaux had enemies like Voltaire and Crebillon, and also because the play has a very violent subtext against the 18th century aristocracy.

## Plot summary

Rosimond is coming from Paris to marry a provincial woman. As he is only obeying his parents who arranged the marriage, he is not really interested in knowing anything about Hortense, his future bride. People say that she has beautiful eyes and has a lot of wits, but Rosimond considers that she must be happy to marry a man like him, desired by all ladies in Paris and belonging to the Royal Court. When he is presented to Hortense, he talks to her with an impertinent tone which appalls her. Hortense decides that she will never marry him if he does not change his manners.

## Characters

* The Count, Hortense's father.
* La Marquise.
* Hortense, the Count's daughter.
* Rosimond, the Marquise's son.
* Dorimène.
* Dorante, friend of Rosimond.
* Marton, Hortense's maid.
* Frontin, Rosimond's valet
# National Route 102 (Costa Rica)

National Secondary Route 102, or just Route 102 (Spanish: Ruta Nacional Secundaria 102, or Ruta 102) is a National Road Route of Costa Rica, located in the San José province.

## Description

In San José province the route covers Vázquez de Coronado canton (San Isidro, Patalillo districts), Tibás canton (San Juan, Anselmo Llorente districts), Moravia canton (San Vicente district).
# Balad Ruz SC

Balad Ruz Sport Club (Arabic: نادي بلدروز الرياضي) is an Iraqi football team based in Balad Ruz, Diyala, that plays in Iraqi First Division League.

## Managerial history

* Hameed Abid Hassan
# Gornja Bitnja

Gornja Bitnja (pronounced; in older sources Bitinje, Italian: Bittigne di Sopra) is a small settlement on the right bank of the Reka River in the Municipality of Ilirska Bistrica in the Inner Carniola region of Slovenia.

## Turn Mansion

There is a 17th-century mansion in the settlement known as Turn Mansion or Turn Radlšek Mansion (Slovene: Turn Radlšek, German: Thurn-Radelsegg). It stands on a hill above the village, and it is an elongated rectangular building with two towers that projecting from it. It dates from the 17th century but was remodeled in the 18th century. There is a pond before the entrance.
# Anita Friedman

Anita Friedman is the executive director of Jewish Family and Children's Services of San Francisco, the Peninsula, Marin & Sonoma Counties in California, one of the largest family service institutions in America. JFCS operates more than 40 educational and social service programs, among them assisted living for seniors, adoption, refugee resettlement, assistance to the disabled, services for victims of abuse, counseling, and mental health and education services for children and youth. Each year, JFCS serves more than 100,000 individuals. JFCS, founded in 1850, is also the oldest charitable organization west of the Mississippi River.

## Biography

Friedman is a noted speaker, philanthropist, activist, and writer on social policy and human services, immigration, and education on the Holocaust and patterns of genocide.
Anita Friedman was born in New York City, attended the University of California at Berkeley, and completed her doctoral degree at the University of San Francisco. Dr. Friedman is a child of Holocaust survivors and lives in San Francisco with her husband and three sons.

## Career

Friedman joined JFCS in 1979. During Friedman's leadership at JFCS, the organization has received national recognition for its programs that include Parents Place, a resource center for new parents and children, Seniors-At-Home, a model continuum of care for frail elderly, and the Center for Children and Youth, providing clinical and educational programs for children, families, clinicians, and educators.
She is the editor of Rywka's Diary, published in English in 2015 by Harper. It is now in print in more than a dozen other languages. She has been an international leader in the provision of innovative human services and active in restoring Jewish life in Poland.
Dr. Friedman has served as a Commissioner of the San Francisco Human Services Commission. She serves on the national board of the American Israel Public Affairs Committee, the Taube Foundation for Jewish Life & Culture, and is President of the Board of Trustees of the Koret Foundation.
She also serves as a Trustee on the Boards of the University of Southern California's Shoah Foundation, the Shalom Hartman Institute of North America, and is Vice President of the International Board of Governors of Tel Aviv University.

## Awards and recognitions

Friedman has received numerous awards, including the San Francisco Business Times Most Influential Women in Business Award, SPUR's Silver Spur Award for civic leadership, the International Louis Kraft Award for professionals in Jewish communal service, Hadassah's highest honor, the Myrtle Wreath Award, Jewish Community Federation's Professional of the Year, the State of California Family Service Council Award, the Koret Prize for leadership in community service, and a distinguished service award from A Wider Bridge.
# Steinernema hermaphroditum

Steinernema hermaphroditum is a species of nematodes in the Steinernematidae family.
It was the first steinernematid reported to be able to self fertilize. The species has been classified as androdioecious.