Feeds:
Posts
Comments

## S07 A combinatorial congruence

07. PEN D2 (Putnam 1991/B4) Suppose that $p$ is an odd prime. Prove that

$\sum_{j = 0}^{p}\binom{p}{j}\binom{p + j}{j}\equiv 2^{p} + 1 \pmod{p^{2}}.$

Here is the official solution file: PEN07sol
You can also disscuss the problems here!

Advertisements