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Right-angled triangle measure of whose sides are integers

Source: IMO Longlist 1989, Problem 24

September 18, 2008
geometryquadraticsnumber theory unsolvednumber theory

Problem Statement

Let a,b,c,d a, b, c, d be positive integers such that ab \equal{} cd and a\plus{}b \equal{} c \minus{} d. Prove that there exists a right-angled triangle the measure of whose sides (in some unit) are integers and whose area measure is ab ab square units.
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