Putnam MODBasic CombinatorialIdentity

Challenging

1991

Problem - 4172

Let $p$ be an odd prime. Show that $$\sum_{j=0}^p\binom{p}{j}\binom{p+j}{j}\equiv 2^p +1 \pmod{p^2}$$

The solution for this problem is available for $0.99.
You can also purchase a pass for all available solutions for $99.