On two supercongruences of double binomial sums

On Sums of Binomial Coefficients

In this paper we study recurrences concerning the combinatorial sum [n r ] m = ∑ k≡r (mod m) (n k ) and the alternate sum ∑ k≡r (mod m)(−1) (n k ) , where m > 0, n > 0 and r are integers. For example, we show that if n > m−1 then b(m−1)/2c ∑ i=0 (−1) (m− 1− i i )[n− 2i r − i ]

on direct sums of baer modules

the notion of baer modules was defined recently

Evaluation of binomial double sums involving absolute values

mostly for small positive integers k, s, t, β. In several cases, they found explicit evaluations of such sums — sometimes with proof, sometimes conjecturally. The purpose of the current paper is to provide a complete treatment of double sums of the form (1.2). More precisely, using the computer algebra package Sigma [13], we were led to the conjecture that these double sums can always be expres...

Binomial Sums and Identities

Generalising Tuenter’s binomial sums

Tuenter [Fibonacci Quarterly 40 (2002), 175-180] and other authors have considered centred binomial sums of the form Sr(n) = ∑