Aptitude Discussion

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 |

**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.

**Pranoy Shit**

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**Arvind**

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

$\frac{N^{P-1}}{P}$ gives the remainder $1$ when $P$ is $prime\ number$ ...

here 7 is a prime number , so the value of $n$ will be $6$