Let a,b,c be three natural numbers such that a<b<c and gcd (c \minus{} a, c \minus{} b) \equal{} 1. Suppose there exists an integer 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 such that c \plus{} d \equal{} l^{2} \plus{} m^{2} .
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