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Number theory - Diophantine equations
3.4 Problems 18.Find two nontrivial solutions to x2 8y2 = 1. 19.Let t n = 1 + 2 + 3 + :::+ n denote the nth triangular number. Find all triangular numbers which are perfect squares. 20. (Putnam 2000/A2) Prove that there exists in nitely many integers n such that n;n+ 1, and n+ 2
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