How would one go about solving the system of five equations:
over the integers? I have no immediate way of answering this question, since it looks to be solved by some "trick." Inequalities may help, although it says "over the INTEGERS" and most inequalities only deal with positive reals.
EDIT: I dont see how congruence's can work, as that may limit the number of solutions, but only to a certain congruence class. For example, we may find that p=1 mod 3, say, but this will only give us an infinite number of p's to check. Unless, of course, we get a congruence contradiction, in which case there would be no solution, but the solution $(3,2,1,5,4)$ works-noted below. (sorry my computer is acting up and wont let me comment)