Number Theory Integers modulo n with addition and multiplication form a commutative ring with the laws of Associativity (a+b)+c= a+(b+c)mod n(also for multiplication) Commutativity atb= bta mod n(also for multiplication) Distributivity (a+b)c=(ac)+(bc)mod n Additive and mul ultiplicative identity a +0= a mod n and a *1=a mod n Additive inverse a+(-a)=0 mod nNumber Theory • Integers modulo n with addition and multiplication form a commutative ring with the laws of – Associativity • (a+b)+c = a+(b+c) mod n (also for multiplication) – Commutativity • a+b = b+a mod n (also for multiplication) – Distributivity • (a+b).c = (a.c)+(b.c) mod n – Additive and Multiplicative identity • a+0 = a mod n and a*1= a mod n – Additive inverse • a+(-a) = 0 mod n