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math.NT2006★ 1 cited
On a special congruence of Carlitz
Sandro Mattarei
We prove that if is a power of a prime and divides , with , then \[ 1+(q-1)\sum_{0\le b(q-1)<a} \binom{a}{b(q-1)}\equiv 0\pmod{p^{k+1}}. \] The special cas…
math.NT2005
Linear recurrence relations for binomial coefficients modulo a prime
Sandro Mattarei
We investigate when the sequence of binomial coefficients \binom{k}{i} modulo a prime p, for a fixed positive integer k, satisfies a linear recurrence relation of (positive) degree…
math.NT2005
Modular periodicity of binomial coefficients
Sandro Mattarei
We prove that if the signed binomial coefficient viewed modulo p is a periodic function of i with period h prime to p in the range , then k+1 is a…