MathNet 2026 — Part 10 Question 179

The sum of the squares of five real numbers $a_{1}, a_{2}, a_{3}, a_{4}, a_{5}$ equals $1$. Prove that the least of the numbers $(a_{i}-a_{j})^{2}$, where $i, j=1,2,3,4,5$ and $i \neq j$, does not exceed $1/10$.