Number Theory Level 3

For positive integers \(a\) and \(b\), it is given that both \(21ab^{2} \) and \(15ab\) are perfect squares. Find \(min(a+b)\)

A perfect square is square of an integer.

Note- I take no credit for this question. This has appeared in \(IMC , RMTC\) and many other contests too.


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