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# What is the remainder when 25 × (1331)^2196 is divided by 13?

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Manager
Joined: 18 Jul 2019
Posts: 54
What is the remainder when 25 × (1331)^2196 is divided by 13?  [#permalink]

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25 Nov 2019, 03:38
2
00:00

Difficulty:

55% (hard)

Question Stats:

53% (01:41) correct 47% (01:52) wrong based on 30 sessions

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What is the remainder when $$25 × (1331)^{2196}$$ is divided by 13?

(A) 0
(B) 1
(C) 7
(D) 11
(E) 12
VP
Joined: 19 Oct 2018
Posts: 1163
Location: India
Re: What is the remainder when 25 × (1331)^2196 is divided by 13?  [#permalink]

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25 Nov 2019, 04:02
1331= 5 mod 13

$$1331^2$$= 25 mod 13= -1 mod 13

$$(1331^2)^{1098}$$= 1 mod 13

$$25 × (1331)^{2196}$$= -1*1 mod 13

$$25 × (1331)^{2196}$$= 12 mod 13

CaptainLevi wrote:
What is the remainder when $$25 × (1331)^{2196}$$ is divided by 13?

(A) 0
(B) 1
(C) 7
(D) 11
(E) 12
Manager
Joined: 10 May 2018
Posts: 57
Re: What is the remainder when 25 × (1331)^2196 is divided by 13?  [#permalink]

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26 Nov 2019, 06:22
1
(26-1)*(1331)^2196/13

26*(1331)^2196/13 - (1331)^2196/13
Remainder

0 - (11)^6588/13

-(13-2)^6588/13
-(-2)^6588/13

-(2^6)^ 1098 /13
-(64)^ 1098 /13
-(65-1)^ 1098 /13
-(-1)^ 1098 /13
-1/13

Remainder is 12
E
Re: What is the remainder when 25 × (1331)^2196 is divided by 13?   [#permalink] 26 Nov 2019, 06:22
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