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m must be a perfect square

Source: IberoAmerican 1987 Q3

November 12, 2010
number theory unsolvednumber theory

Problem Statement

Prove that if m,n,rm,n,r are positive integers, and: 1+m+n3=(2+3)2r−11+m+n\sqrt{3}=(2+\sqrt{3})^{2r-1} then mm is a perfect square.
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