What do you need help with? Are you having trouble applying the hint? Do you have any work done that we can look at? If you are looking for a place to start, choose a couple values for p and see what is going on. For example, check out the integers in {0,1,2} of the form x^2 modulo 3 and those of the form -1-y^2 modulo 3. Try it for 5 and 7 also. Do you notice any patterns? Try to show that the number of integers of that form is greater than . Then by the pigeonhole principle, there must be some x^2 and -1-y^2 that are congruent modulo p.

For (b), what is m?