On the Golomb’s conjecture and Lehmer’s numbers

Wang Tingting; Wang Xiaonan

Displaying similar documents to “On the Golomb’s conjecture and Lehmer’s numbers”

On congruence conditions for primality.

Gong, Sherry, Kominers, Scott Duke (2010)

Integers

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On the congruence f(x) + g(y) + c ≡ 0 (mod xy) (completion of Mordell's proof)

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.

Proof of a conjecture of Hirschhorn and Sellers on overpartitions

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)...