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Remainder - Problem Solving

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Remainder - Problem Solving  [#permalink]

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New post 06 Oct 2018, 04:21
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N=56^56+56. What would be the remainder when N is divided by 57?

What i did was: N/57=(57-1)^56/57+(57-1)/57

Doing this would give me the remainder as 2.

But, if we do it like this: (57-1)^56/57 would give remainder 1 and adding it to 56, we have 57. Thus the final remainder would be 0.

Which approach do you think is correct?
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Re: Remainder - Problem Solving  [#permalink]

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New post 06 Oct 2018, 05:49
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akshit1993 wrote:
N=56^56+56. What would be the remainder when N is divided by 57?

What i did was: N/57=(57-1)^56/57+(57-1)/57

Doing this would give me the remainder as 2.

But, if we do it like this: (57-1)^56/57 would give remainder 1 and adding it to 56, we have 57. Thus the final remainder would be 0.

Which approach do you think is correct?



Both are correct. Little calculation mistake in your first approach(Highlighted).

When (57-1) is divided by 57. You get a negative remainder of -1. Since remainder cannot be negative. Convert it to positive by adding the divisor to -1. remainder becomes -1+57 = 56. You end with 1+56, which gives a remainder 0 when divided by 57.

Hope it's clear.
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Re: Remainder - Problem Solving &nbs [#permalink] 06 Oct 2018, 05:49
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