Primes in their prime
Given that is a prime number, and the sum of positive divisors of is a perfect square, find the number of possible integer solutions for .
The answer is 1.
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1 solution
If 1 + p + p 2 + p 3 + p 4 = y 4 , we can show that p 2 < y < p 2 + p , but since y is congruent to +-1 mod p, there are only two cases to consider.The only sol is p=3.