Linear recurrence relations for binomial coefficients modulo a prime Original Research Article

We investigate when the sequence of binomial coefficients image modulo a prime p, for a fixed positive integer k, satisfies a linear recurrence relation of (positive) degree h in the finite range 0less-than-or-equals, slantiless-than-or-equals, slantk. In particular, we prove that this cannot occur if 2hless-than-or-equals, slantk