Question

Evaluate the following
a) 5 ÷ 2 (mod 6)
b) 9 ÷ 7 (mod 7)
c) 3 × 2 ÷ 5 (mod 7)​

Answer 1

Neither 2 nor 7 have inverses mod 6 or 7, respectively, so the expressions in (a) and (b) cannot really evaluated... At least we can evaluate (c) :

`5*3 \equiv 15 \equiv 1 \pmod 7 \\\\ \implies 3*2/5 \equiv 3*2*3 \equiv18 \equiv \boxed{4 \pmod{7}}`