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Problem 2 of RMO 2007 (Regional Mathematical Olympiad-India)

Source: Pythagorean triple

September 13, 2009
number theorygreatest common divisorsearchnumber theory unsolved

Problem Statement

Let a,b,c a, b, c be three natural numbers such that a<b<c a < b < c and gcd (c \minus{} a, c \minus{} b) \equal{} 1. Suppose there exists an integer d d such that a \plus{} d, b \plus{} d, c \plus{} d form the sides of a right-angled triangle. Prove that there exist integers, l,m l,m such that c \plus{} d \equal{} l^{2} \plus{} m^{2} . [Weightage 17/100]
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