What is the remainder when 7^9 - 4 is divided by 7?

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What is the remainder when 7^9 - 4 is divided by 7? [#permalink]

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14 Apr 2017, 03:32

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What is the remainder when 7^9 - 4 is divided by 7?

A)1
B)2
C)3
D)4
E)5

Spoiler: OA

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Re: What is the remainder when 7^9 - 4 is divided by 7? [#permalink]

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14 Apr 2017, 03:36

amathews wrote:

What is the remainder when 7^9 - 4 is divided by 7?

A)1
B)2
C)3
D)4
E)5

7^9 - 4 = {a multiple of 7} - 4, so it's 4 less than a multiple of 7 (3, 10, 17, ...), so the remainder is 3.

Answer: C.
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Re: What is the remainder when 7^9 - 4 is divided by 7? [#permalink]

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14 Apr 2017, 05:27

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amathews wrote:

What is the remainder when 7^9 - 4 is divided by 7?

A)1
B)2
C)3
D)4
E)5

If we take 7^9 - 4 and zero to it, the value doesn't change.
We're going to add zero by subtracting 3 and adding 3 at the same time.
So, 7^9 - 4 = 7^9 - 4 - 3 + 3
= 7^9 - 7 + 3
= 7(7^8 - 1) + 3
= 7(some integer) + 3

As we can see, our initial number can be rewritten as 3 more than some multiple of 7.
So, if we divide that number by 7, the remainder will be 3

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14 Apr 2017, 06:00

amathews wrote:

What is the remainder when 7^9 - 4 is divided by 7?

A)1
B)2
C)3
D)4
E)5

\(\frac{7^9 - 4}{7}\)

\(= Rem ( 0 - 4 )\)

So, We have remainder -4

Thus, the value of the remainder will be \(7 - 4 = 3\)

Answer, must be (C) 3
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Re: What is the remainder when 7^9 - 4 is divided by 7? [#permalink]

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14 Apr 2017, 07:29

Bunuel wrote:

amathews wrote:

What is the remainder when 7^9 - 4 is divided by 7?

A)1
B)2
C)3
D)4
E)5

7^9 - 4 = {a multiple of 7} - 4, so it's 4 less than a multiple of 7 (3, 10, 17, ...), so the remainder is 3.

Answer: C.

Hello Bunnel.
When it is 7^8 -4 then what would be remainder. Thanks in advance.

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Re: What is the remainder when 7^9 - 4 is divided by 7? [#permalink]

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14 Apr 2017, 07:35

Chemerical71 wrote:

Bunuel wrote:

amathews wrote:

What is the remainder when 7^9 - 4 is divided by 7?

A)1
B)2
C)3
D)4
E)5

7^9 - 4 = {a multiple of 7} - 4, so it's 4 less than a multiple of 7 (3, 10, 17, ...), so the remainder is 3.

Answer: C.

Hello Bunnel.
When it is 7^8 -4 then what would be remainder. Thanks in advance.

It seems that you did not understand the explanation. The remainder of 7^n - 4 divided by 7 where n is a positive integer is always 3.
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Re: What is the remainder when 7^9 - 4 is divided by 7? [#permalink]

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19 Jan 2019, 09:28

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Re: What is the remainder when 7^9 - 4 is divided by 7? [#permalink] 19 Jan 2019, 09:28