Modular periodicity of binomial coefficients Original Research Article

We prove that if the signed binomial coefficient image viewed modulo p is a periodic function of i with period h in the range 0less-than-or-equals, slantiless-than-or-equals, slantk, then k+1 is a power of p, provided h is not too large compared to k. (In particular, 2hless-than-or-equals, slantk suffices). As an application, we prove that if G and H are multiplicative subgroups of a finite field, with H