VTMO 2026 - Grade 7 - Final - SET 5 - Self-study Question 2

Natural numbers $a_1,a_2,\ldots,a_{100}$ satisfy $\frac1{a_1}+\frac1{a_2}+\cdots+\frac1{a_{100}}=\frac{101}{2}$. Prove that at least two of the numbers are equal.