MathDB

1

Part of 1994 USAMO

Problems(1)

Classic algebra problem

Source: USAMO1994

8/22/2005
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.
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