MathDB
Classic algebra problem

Source: USAMO1994

August 22, 2005
LaTeXnumber theory unsolvednumber theory

Problem Statement

Let  k1<k2<k3<⋯ \, k_1 < k_2 < k_3 < \cdots \, be positive integers, no two consecutive, and let  sm=k1+k2+⋯+km \, s_m = k_1 + k_2 + \cdots + k_m \, for  m=1,2,3,…    \, m = 1,2,3, \ldots \; \;. Prove that, for each positive integer  n, \, n, \, the interval  [sn,sn+1) \, [s_n, s_{n+1}) \, contains at least one perfect square.
Back to ProblemsView on AoPS