Let q > 1 and m > 0 be relatively prime integers. We find an explicit period v(m)(q) such that for any integers n > 0 and r we have [GRAPHICS] whenever a is an integer with gcd (1 - (-a)(m), q) = 1, or a = -1 (mod q), or a 1 (mod q) and 2 vertical bar m, where [GRAPHICS] This is a further extension of a congruence of Glaisher. (C) 2007 Elsevier Inc. All rights reserved.
Sun, Z., Tauraso, R. (2007). Congruences for sums of binomial coefficients. JOURNAL OF NUMBER THEORY, 126(2), 287-296 [10.1016/j.jnt.2007.01.002].
Congruences for sums of binomial coefficients
TAURASO, ROBERTO
2007-01-01
Abstract
Let q > 1 and m > 0 be relatively prime integers. We find an explicit period v(m)(q) such that for any integers n > 0 and r we have [GRAPHICS] whenever a is an integer with gcd (1 - (-a)(m), q) = 1, or a = -1 (mod q), or a 1 (mod q) and 2 vertical bar m, where [GRAPHICS] This is a further extension of a congruence of Glaisher. (C) 2007 Elsevier Inc. All rights reserved.File in questo prodotto:
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