Prove that , for most of the primes $\displaystyle p$ , $\displaystyle \binom{kp}{p} \equiv k \bmod{p^3} , k \in \mathbb{N} $ and also find all the exceptional prime(s) .

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- Jun 28th 2010, 07:43 PMsimplependulumA problem about binomial coefficient
Prove that , for most of the primes $\displaystyle p$ , $\displaystyle \binom{kp}{p} \equiv k \bmod{p^3} , k \in \mathbb{N} $ and also find all the exceptional prime(s) .