Some congruences for binomial coefficients
Tsuneo Ishikawa (2006)
Acta Arithmetica
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Tsuneo Ishikawa (2006)
Acta Arithmetica
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L. Carlitz (1959/60)
Mathematische Zeitschrift
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Francisco Thaine (1991)
Manuscripta mathematica
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Bóna, Miklós, Sagan, Bruce E. (2005)
Journal of Integer Sequences [electronic only]
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Pierre Kaplan, Kenneth Williams (1982)
Acta Arithmetica
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John B. Cosgrave, Karl Dilcher (2010)
Acta Arithmetica
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Müller, Tom (2005)
Integers
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Zhi-Wei Sun (2007)
Acta Arithmetica
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Vsemirnov, M. (2004)
Journal of Integer Sequences [electronic only]
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L. Carlitz, W.A. Al-Salam (1958)
Monatshefte für Mathematik
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Sanoli Gun (2010)
Acta Arithmetica
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Roberto Tauraso (2013)
Colloquium Mathematicae
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We establish q-analogs for four congruences involving central binomial coefficients. The q-identities necessary for this purpose are shown via the q-WZ method.
Song Heng Chan (2012)
Acta Arithmetica
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Chris Jennings-Shaffer (2016)
Acta Arithmetica
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We continue to investigate spt-type functions that arise from Bailey pairs. In this third paper on the subject, we proceed to introduce additional spt-type functions. We prove simple Ramanujan type congruences for these functions which can be explained by an spt-crank-type function. The spt-crank-type functions are actually defined first, with the spt-type functions coming from setting z = 1 in this definition. We find some of the spt-crank-type functions to have interesting representations...
S. Lewanowicz (1983)
Applicationes Mathematicae
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Tao Yan Zhao, Lily J. Jin, C. Gu (2016)
Open Mathematics
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Let p3(n) denote the number of 3-component multipartitions of n. Recently, using a 3-dissection formula for the generating function of p3(n), Baruah and Ojah proved that for n ≥ 0, p3(9n + 5) ≡ 0 (mod 33) and p3 (9n + 8) ≡ 0 (mod 34). In this paper, we prove several congruences modulo powers of 3 for p3(n) by using some theta function identities. For example, we prove that for n ≥ 0, p3 (243n + 233) ≡ p3 (729n + 638) ≡ 0 (mod 310).
Stanley Burris (1971)
Colloquium Mathematicae
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