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# What is the remainder when 81^82 is divided by 17?

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Manager
Joined: 18 Jul 2019
Posts: 54
What is the remainder when 81^82 is divided by 17?  [#permalink]

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24 Nov 2019, 12:28
7
00:00

Difficulty:

55% (hard)

Question Stats:

43% (01:19) correct 57% (01:59) wrong based on 23 sessions

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What is the remainder when $$81^{82}$$ is divided by 17?

(A) 1
(B) 4
(C) 13
(D) 15
(E) 16
VP
Joined: 19 Oct 2018
Posts: 1171
Location: India
Re: What is the remainder when 81^82 is divided by 17?  [#permalink]

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24 Nov 2019, 13:27
81=-4 mod 17

$$81^{82}$$= $$(-4)^{82}$$ mod 17

$$81^{82}$$= $$(16)^{41}$$ mod 17

$$81^{82}$$= $$(-1)^{41}$$ mod 17

$$81^{82}$$= -1 mod 17

$$81^{82}$$= (17-1) mod 17

$$81^{82}$$= 16 mod 17

CaptainLevi wrote:
What is the remainder when $$81^{82}$$ is divided by 17?

(A) 1
(B) 4
(C) 13
(D) 15
(E) 16
Re: What is the remainder when 81^82 is divided by 17?   [#permalink] 24 Nov 2019, 13:27
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