Problem

Source: Mongolia TST 2011 Test 1 #2

Tags: Putnam, function, number theory unsolved, number theory



Mongolia TST 2011 Test 1 #2 Let p be a prime number. Prove that: \sum_{k=0}^p (-1)^k \dbinom{p}{k} \dbinom{p+k}{k} \equiv -1 (\mod p^3) (proposed by B. Batbayasgalan, inspired by Putnam olympiad problem) Note: I believe they meant to say p>2 as well.