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Remainder when 25^10 is divided by 576?

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Remainder when 25^10 is divided by 576?  [#permalink]

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New post 14 Oct 2018, 05:24
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A
B
C
D
E

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(N/A)

Question Stats:

67% (02:07) correct 33% (02:03) wrong based on 3 sessions

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a) 241
b) 341
c) 571
d) 680
e) None of these

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Remainder when 25^10 is divided by 576?  [#permalink]

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New post 14 Oct 2018, 05:42
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asifahmed500 wrote:
a) 241
b) 341
c) 571
d) 680
e) None of these

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We need to find out the remainder of 25^10 when divided by 576.
Please note that 576 = 24^2


Using Binomial Theorem

25^10 = (24 + 1)^10
In the expansion, there will be 11 terms where the powers of 24 will vary from 0 to 10.
If the power of 24 is greater than or equal to 2 in a term, that term will be divisible by 576
The terms that will not be divisible by 576 are the terms that have powers of 24 as 0 or 1.
Those terms are
10C1*24^1*1^9 + 10C0*24^0*1^10
= 10*24*1 + 1*1*1
= 241

So, Rem [25^10/576] = 241


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Re: Remainder when 25^10 is divided by 576?  [#permalink]

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New post 14 Oct 2018, 05:44
Is it possible to solve power of cyclicity approach

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Re: Remainder when 25^10 is divided by 576?   [#permalink] 14 Oct 2018, 05:44
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Remainder when 25^10 is divided by 576?

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