Question 43
Do there exist positive integers $n$ and $k$, $1 \le k \le n-2$, such that
$$
\binom{n}{k}^2 + \binom{n}{k+1}^2 = \binom{n}{k+2}^4 ?
$$
$$
\binom{n}{k}^2 + \binom{n}{k+1}^2 = \binom{n}{k+2}^4 ?
$$
MathNet 2011 Question 43
Math Olympiad Vault · MathNet 2011