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Question: Answered & Verified by Expert
If $a, b$ are natural numbers such that $2013+a^{2}=b^{2}$, then the minimum possible value of $a b$ is
MathematicsBasic of MathematicsKVPYKVPY 2013 (SA)
Options:
  • A $671$
  • B $668$
  • C $658$
  • D $645$
Solution:
2041 Upvotes Verified Answer
The correct answer is: $658$
$(b-a)(b+a)=2013=3 \times 11 \times 61$
$ab$ minimum when $b-a=33$
$\begin{array}{l}
b+a=61 \\
a=14
\end{array}$
$a b=14 \times 47=658$

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