(a) If n=3, determine all integer values of m such that m^{2}+n^{2}+1 is divisible by m-n+1 and m+n+1.
(b) Show that for any integer n there is always at least one integer value of m for which m^{2}+n^{2}+1 is divisible by both m-n+1 and m+n+1.
(c) Show that for any integer n there are only a finite number of integer values m for which m^{2}+n^{2}+1 is divisible by both m-n+1 and m+n+1.