Question 60
Let $p$ be a prime number. Prove that
$$
\sum_{k=0}^{p} (-1)^k \binom{p}{k} \binom{p+k}{k} \equiv -1 \pmod{p^3}
$$
$$
\sum_{k=0}^{p} (-1)^k \binom{p}{k} \binom{p+k}{k} \equiv -1 \pmod{p^3}
$$
MathNet 2010 — Part 04 Question 60
Math Olympiad Vault · MathNet 2010 — Part 04