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Q.

For what value of '$n$' will the remainder of $351^n$ and $352^n$ be the same when divided by 7?

 A.

2

 B.

3

 C.

6

 D.

4

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Solution:
Option(B) is correct

When 351 is divided by 7, the remainder is 1.

When 352 is divided by 7, the remainder is 2.

Let us look at answer choice (1), $n = 2$

When $351^2$ is divided by 7, the remainder will be $1^2 = 1$.

When $352^2$ is divided by 7, the remainder will be $2^2 = 4$. 

So when $n = 2$, the remainders are different.

When $n = 3$, 

When $351^3$ is divided by 7, the remainder will be $1^3 = 1$.

When $352^3$ is divided by 7, the remainder will be $2^3 = 8$. 

As 8 is greater than 7, divide 8 again by 7, the new remainder is 1.

So when $n=3$, both $351^n$ and $352^n$ will have the same remainder when divided by 7.


(1) Comment(s)


Arvind
 ()

Here 6 can also be the answer as $2^6$ when divided by 7 also gives the remainder 1