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At least one square between T_n-1 and T_n - JBMO Shortlist

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October 30, 2010
number theory proposednumber theory

Problem Statement

Let xk=k(k+1)2x_k=\frac{k(k+1)}{2} for all integers k≥1k\ge 1. Prove that for any integer n≥10n \ge 10, between the numbers A=x1+x2+…+xn−1A=x_1+x_2 + \ldots + x_{n-1} and B=A+xnB=A+x_n there is at least one square.
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