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If  135013^{50}1350​ is divided by 14, the remainder is -
Question

If  135013^{50}​ is divided by 14, the remainder is -

A.

13

B.

12

C.

1

D.

- 1

Correct option is C

Given:
135013^{50}​ is divided by 14.
Concept used:
When (p – 1)ⁿ is divided by p, the remainder will be 1 only if n is an even number.
Solution:
1350 can be written as (14 – 1)⁵⁰.
Here, p = 14 and n = 50.
Since 50 is an even number,
when (14 – 1)⁵⁰ is divided by 14, the remainder = 1.
Correct answer is (c) 1.

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