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What will be the remainder when is divided by 266?
Question

What will be the remainder when is divided by 266?

A.

8

B.

6

C.

1

D.

9

Correct option is A

Given:

We need to find the remainder when (265)4081+9 (265)^{4081} + 9​ is divided by 266.
Concept Used:
Since 265 is just 1 less than 266, we can simplify the expression using the property of powers and moduli:
(265)4081mod 266(265)^{4081} \mod 266​​
is equivalent to:
(1)4081mod 266(-1)^{4081} \mod 266​​
Solution:
Since 4081 is an odd number:
(1)4081=1(-1)^{4081} = -1​​
Thus, the expression becomes:
(265)4081+9=1+9=8(265)^{4081} + 9 = -1 + 9 = 8​​
Therefore, the remainder when  is divided by 266 is 8.
​​

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