Congruences for sums of binomial coefficients

Zhi-Wei Sun, Roberto Tauraso

Let q>1 and m>0 be relatively prime integers. We find an explicit period ${\nu }_m(q)$ such that for any integers n>0 and r we have $[n+{\nu }_m(q),r{]}_m(a)=[n,r{]}_m(a)(modq)$ whenever a is…