Congruence properties of paritions
S., Ramanujan (1921)
Mathematische Zeitschrift
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S., Ramanujan (1921)
Mathematische Zeitschrift
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Gong, Sherry, Kominers, Scott Duke (2010)
Integers
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A. Schinzel (2015)
Acta Arithmetica
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Assertions on the congruence f(x) + g(y) + c ≡ 0 (mod xy) made without proof by Mordell in his paper in Acta Math. 88 (1952) are either proved or disproved.
A. Schinzel (2016)
Banach Center Publications
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Four theorems of the author on the subject are given without proofs.
William Y. C. Chen, Ernest X. W. Xia (2014)
Acta Arithmetica
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Let p̅(n) denote the number of overpartitions of n. It was conjectured by Hirschhorn and Sellers that p̅(40n+35) ≡ 0 (mod 40) for n ≥ 0. Employing 2-dissection formulas of theta functions due to Ramanujan, and Hirschhorn and Sellers, we obtain a generating function for p̅(40n+35) modulo 5. Using the (p, k)-parametrization of theta functions given by Alaca, Alaca and Williams, we prove the congruence p̅(40n+35) ≡ 0 (mod 5) for n ≥ 0. Combining this congruence and the congruence p̅(4n+3)...
Sydney Bulman-Fleming (1971)
Mathematische Zeitschrift
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Xu, Ping, Pan, Hao (2007)
Integers
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Jerzy Urbanowicz (1994)
Compositio Mathematica
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Scott Ahlgren (2003)
Acta Arithmetica
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Manfred Armbrust (1973)
Colloquium Mathematicae
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Getz, Jayce (2000)
International Journal of Mathematics and Mathematical Sciences
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Kiss, Elemér, Sándor, József (2004)
Mathematica Pannonica
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Marica D. Prešić (1979)
Publications de l'Institut Mathématique
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Hao Pan (2007)
Acta Arithmetica
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Leonard Eugene Dickson (1901)
Mathematische Annalen
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Ying Zhang (2007)
Acta Arithmetica
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