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

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

$$\frac{7^9 - 4}{7}$$

$$= Rem ( 0 - 4 )$$

So, We have remainder -4

Thus, the value of the remainder will be $$7 - 4 = 3$$

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

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]
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.

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

(7^9-4)mod7 = -4mod7 = 3mod7

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Re: What is the remainder when 7^9 - 4 is divided by 7? [#permalink]
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Can anyone please explain it again in simple terms. I am still not able to understand it. May be i am missing something here.
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Re: What is the remainder when 7^9 - 4 is divided by 7? [#permalink]
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We need to find What is the remainder when $$7^9$$ - 4 is divided by 7

$$7^9$$ - 4 = $$7^9$$ - 4 - 3 + 3 = $$7^9$$ - 7 + 3 = 7*($$7^8$$ - 1) + 3 = (Multiple of 7) + 3

Theory: Remainder of a + b by a number say 7 is same as remainder of a by 7 + remainder of b by 7

=> Remainder of 7*($$7^8$$ - 1) + 3 by 7 is same as remainder of 7*($$7^8$$ - 1) by 7 + remainder of 3 by 7

=> 0 + 3 = 3

Hope it helps!

Watch the following video to learn the Basics of Remainders

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