[frankmcsherry]

To be pedantic, shouldn't you also need to rule out the possibility that x is a negative number? For example, x = -1 satisfies your quadratic equation, but because we are doing an odd power of x you can rule it out.

[amluto]

Aside from the 1 vs -1 issue, the proof finds all integers x such that p is prime. So I think it’s fine.