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Part of 2007 Estonia Math Open Senior Contests

Problems(1)

Estonian Math Competitions 2006/2007

Source: Seniors Problem 1

Let a_n \equal{} 1 \plus{} 2 \plus{} ... \plus{} n for every

n \ge 1

a_n

are called triangular. Prove that if 2a_m \equal{} a_n then a_{2m \minus{} n} is a perfect square.

number theory unsolvednumber theory