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.