Where x is an element of integers, show that for x=x^2 that 0 or 1 are the only solutions to this equation. I have shown that 0 and 1 are solutions to this, but I am trying to show that no other solutions are possible. My plan was to show that no negative number could be a solution to this problem because two negatives would make a positive and this could never equal a negative number. And I also showed that for any number greater than 1 that this equation could never be true because the right hand side would always be greater. I am having trouble doing this expressing the first five axioms, or if it is not possible to prove this with the first five, then maybe the first 6. I am not sure how to account for greater than or less than relations yet. Thanks for reading this whole thing.