Find all prime numbers P such that p * (p-1 power-1 of 2) is the K power of a positive integer, k > 1 and K is a positive integer

Prime number P can be divided into two types: even number 2 and odd number form (2a + 1). 1. When p = 2, 2 * (2 ^ 1 - 1) = 2 obviously can't be written to the K power of a positive integer; 2. When p = 2A + 1, a ∈ Z + (2a + 1) * [2 ^ (2a) - 1] = (2a + 1) * (2 ^ A - 1) * (2 ^ A + 1) - ------- 1, because (2 ^ A - 1

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