MathLabs

Problem 6

Let a>b>c>d>0 a>b>c>d>0 be integers satisfying ac+bd=(b+d+a−c)(b+d−a+c) ac+bd=(b+d+a-c)(b+d-a+c). Prove that ab+cd ab+cd is not prime.
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p=ab+cd>ac+bd>ad+bc>0.p=ab+cd>ac+bd>ad+bc>0.
Detailed analysis

The strict inequalities follow from a greater than b greater than c greater than d.