What is the minimum value of p for which 1/532900 + p²/266450 + p⁴/523900 is an integer?

For the sum to be an integer, p must be chosen so that all three fractions combine to an integer. The denominators 532900, 266450, 523900 contain various prime factors. The smallest p making the expression an integer, based on the LCM structure of the denominators and the requirement that p² and p⁴ clear the denominators, is p = 729 = 3⁶.