Congruences for sums of binomial coefficients

✍ Scribed by Zhi-Wei Sun; Roberto Tauraso

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 135 KB
• Volume: 126
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2007.01.002

✦ Synopsis

Let q > 1 and m > 0 be relatively prime integers. We find an explicit period ν m (q) such that for any integers n > 0 and r we have

whenever a is an integer with gcd(1 -(-a) m , q) = 1, or a ≡ -1 (mod q), or a ≡ 1 (mod q) and 2 | m, where n r m (a) = k≡r (mod m) n k a k . This is a further extension of a congruence of Glaisher.