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If a and b are positive integers, what is the remainder when 74a+b is

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Senior SC Moderator
Joined: 14 Nov 2016
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Location: Malaysia
If a and b are positive integers, what is the remainder when 74a+b is  [#permalink]

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24 Mar 2017, 04:40
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35% (medium)

Question Stats:

73% (01:32) correct 27% (01:34) wrong based on 66 sessions

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If a and b are positive integers, what is the remainder when $$7^{4a}+b$$ is divided by 4?

1) a=2
2) b=3

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Joined: 13 Oct 2016
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Re: If a and b are positive integers, what is the remainder when 74a+b is  [#permalink]

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24 Mar 2017, 07:36
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ziyuen wrote:
If a and b are positive integers, what is the remainder when $$7^{4a}+b$$ is divided by 4?

1) a=2
2) b=3

Hi

$$7^{4a} + b$$

$$7^2$$ leaves remainder $$1$$ when divided by $$4$$ ------> $$(7^2)^{2a} + b = 1^{2a} + b = 1 + b$$

To solve the question we need to know only the remainder that $$b$$ leaves while divided by $$4$$.

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Joined: 08 Sep 2015
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Re: If a and b are positive integers, what is the remainder when 74a+b is  [#permalink]

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24 Mar 2017, 09:07
To solve this question, have to remember the last digit of a power...for 7 the cyclicity is 7,9,3,1 -> since a is a positive integer, the 7^4a will always end with 1 and we know that a number is divisible by 4 when the last two digits are divisible by 4.

A) Irrelevant -> not sufficient
B) since we know b, we know the last digit of our number, therefore can find the remainder. Sufficient.
Re: If a and b are positive integers, what is the remainder when 74a+b is &nbs [#permalink] 24 Mar 2017, 09:07
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If a and b are positive integers, what is the remainder when 74a+b is

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