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S.O.S. is not a prime (Posted on 2017-02-15)

Prove that:
if for integers a,b,c,d
a*d= b²+b*c+c²
then:
a²+b²+ c² + d²
is a composite number.

No Solution Yet Submitted by Ady TZIDON

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Factorization

Comment 1 of 1

Rearrange the given identity into ad - bc - b^2 - c^2 = 0

Then a^2 + b^2 + c^2 + d^2

= a^2 + b^2 + c^2 + d^2 + 2*(ad - bc - b^2 - c^2)

= a^2 - 2ad + d^2 - b^2 - 2bc - c^2

= (a-d)^2 - (b+c)^2

= (a+b+c-d) * (a-b-c-d)

This will be composite as long as neither factor is -1, 0, or 1.

Posted by Brian Smith on 2018-12-15 23:48:14

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