Question 22
Determine all pairs $(n, k)$ of integers such that $0 \lt k \lt n$ and
$$
\binom{n}{k-1} + \binom{n}{k+1} = 2 \binom{n}{k}
$$
$$
\binom{n}{k-1} + \binom{n}{k+1} = 2 \binom{n}{k}
$$
MathNet 2026 — Part 10 Question 22
Math Olympiad Vault · MathNet 2026 — Part 10