IMO 1978 LL USA43

If p is a prime greater than 3, show that at least one of the

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IMO 1978 LL USA43

Origin: USA

Problem

If p is a prime greater than 3, show that at least one of the numbers p2 , 4 p2 , . . . , p−2 p2 is expressible in the form 1 x + 1 y, where x and y are positive integers.