Explanation

The expression equals (1 + 2p² + p⁴)/532900 = (p²+1)²/532900, and 532900 = 730². For this to be an integer, 730 must divide p² + 1. The smallest p with 730 | (p²+1) is p = 27, since 27² + 1 = 730 (any smaller p gives p² + 1 < 730, which cannot be a multiple of 730). Hence the minimum p is 27, option (c).