Exercise 1. This software finds all solutions to the equation \(x^2 + y^2 = 0\) in \(Z_p\). Run your program for all odd primes up to \(37\). Make a conjecture about the the number of solutions in \(Z_p\) (where \(p\) is a prime) and the form of \(p\).

Please enter a prime \(p\) and click the button, the solutions will show below.