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British Mathematical Olympiad , 1991 , two problems on perfect squares:1) Problem 1 , and generalizations. 2)Problem 6: Show that if x and y are positive integers such that x^2 + y^2 - x is divisible by 2xy , then x is a perfect square.

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Publication Date: October 14 , 2019 Number of Pages: 17 The subject matter of this paper , is two problems on perfect squares that were featured in the 1991 British Mathematical Olympiad. Let us first state the two problems. Both problems are
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