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diophantine ab =2(1 + cd), exists a triangle with sides a - c, b - d and c + d

Source: 2022 Dutch IMO TST 3.1

December 3, 2022
number theoryDiophantine equationdiophantine

Problem Statement

Find all quadruples (a,b,c,d)(a, b, c, d) of non-negative integers such that ab=2(1+cd)ab =2(1 + cd) and there exists a non-degenerate triangle with sides of length a−ca - c, b−db - d, and c+dc + d.
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