A number theory problem by Márcio Nascimento

Number Theory Level pending

A rectangle has integer perimeter P and integer area A and integer sides. If

P + 4 P 4 = A 1 \\ \frac { P+4 }{ P-4 } =A-1\\

then what is the sum of all possible perimeters and areas?

Original problem link


The answer is 12.

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