What is the remainder when $32^{32}$ is divided by 3

Question

What is the remainder when $32^{32}$ is divided by 3 ?

MY ATTEMPT

$$32^{32}=(2)^{160}$$

$$32^{32}=(3-1)^{160}$$

$$32^{32}=3M+(-1)^{160}$$

According to binomial expansion $$32^{32}=3M+1$$

Thus the remainder is 1.

Am I correct ?

Such questions have been answered here already often, see for example here. Bill's answer solves your question, too. — Dietrich Burde, Mar 24 '20 at 17:43

score 1 · Accepted Answer · answered Mar 24 '20 at 17:36

1

Yes, that works. Similarly

$$32^{32}=(33-1)^{32}=33M+(-1)^{32}=3\times 11M+1$$

so the remainder is $1$

answered Mar 24 '20 at 17:36

Henry

1 Answers1