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

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

IMO C
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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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We need to find What is the remainder when \(7^9\) - 4 is divided by 7

Remainder of \(7^9\) - 4 by 7 = Remainder of \(7^9\) by 7 + Remainder of -4 by 7 = 0 + -4 = -4

=> Remainder = -4 + 7 = 3

So, Answer will be C
Hope it helps!

Watch following video to MASTER Remainders by 2, 3, 5, 9, 10 and Binomial Theorem

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