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 1 of 6: Rewrite
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a2−ac+c2=b2+bd+d2.a^2-ac+c^2=b^2+bd+d^2.
Detailed analysis

Expand the hypothesis and rearrange.