Multiplicative Inverses and Congruence equations When does a number has a multiplicative inverse? When does a congruence equation ax= b mod m has a solution has a unique solution 5X=8mod12=>x=4 3x=8 mod 12==> no solution 3x=9mod12=>xin{3,7,11}Multiplicative Inverses and Congruence Equations • When does a number has a multiplicative inverse? • When does a congruence equation ax = b mod m – has a solution – has a unique solution • 5x = 8 mod 12 ==> x = 4 • 3x = 8 mod 12 ==> no solution • 3x = 9 mod 12 ==> x in {3,7,11}