Thread: A proof in abstract algebra

Prove that if p is a prime and c is not congruent 0 (mod p), then cx is congruent b (mod p) has a unique solutin modulo p. That is, a solution exists, and any two solutions are congruent modulo p.

Originally Posted by rainyice

Prove that if p is a prime and c is not congruent 0 (mod p), then cx is congruent b (mod p) has a unique solutin modulo p. That is, a solution exists, and any two solutions are congruent modulo p.

If there exists such that then this means that , by definition of congruence. So, . As then . Thus, .

Originally Posted by Swlabr

If there exists such that then this means that , by definition of congruence. So, . As then . Thus, .

you are very helpful ~ thank you ^_^