GATE 2026 EE – Question 10
$P$ and $Q$ are two positive integers such that $P^2=Q^2+13$.
The product of the numbers $P$ and $Q$ is ________.
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Correct answer: (D) 42
Explanation
$P^2-Q^2=(P-Q)(P+Q)=13$, and 13 is prime, so $P-Q=1$ and $P+Q=13$. Then $P=7$, $Q=6$ and $PQ=42$.