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

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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 ?

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1 Answer

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Yes, that works. Similarly

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

so the remainder is $1$

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