What is the <strong>MINIMUM</strong> value of p for which \frac{1}{532900}+\frac{p^{2}}{266450}+\frac{p^{4}}{523900} is an integer?

Explanation

Assuming the third denominator is a typo for 532900, the expression simplifies to \frac{1 + 2p^2 + p^4}{532900} = \frac{(p^2+1)^2}{730^2}. For this to be an integer, p^2+1 must be a multiple of 730. Therefore, p^2 = 729, which means p=27.

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