(c) show that if p is any polynomial with integer coefficients, and if a = b (mod m), then p(a) = p(b) (mod m). 6. let me n, and a, b e z. consider the problem of solving the follow- ing congruence ar = b (mod m). a solution is any number k for which ak – b is divisible by m. (a) show that 7 is a solution of the congruence 4x = 3 (mod 5). find all other solutions of this congruence. (b) find all solutons of the congruences (i) 4x = 3 (mod 6) (ii) 4x = 2 (mod 6). (c) let g = gcd(a, m). show that, if ar = b (mod m) has a solution, then g|b. (d) conversely, show that if a gcdlem) and alh then the con-