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.
Step 6 of 6: Conclude
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ab+cd is not prime.ab+cd\text{ is not prime}.
Detailed analysis

This contradiction proves the assertion.