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The remainder when the number 3^(256) - ...

The remainder when the number `3^(256) - 3^(12)` is divided by 8 is (a) 0 (b) 3 (c) 4 (d) 7

A

0

B

3

C

4

D

7

Text Solution

Verified by Experts

The correct Answer is:
A
`3^(256)-3^(12)=3^(12)(3^(244)-1)`
`=(1+8)^(6)((1+8)^(122)-1)`
`=(1+8lambda)(1+8mu-1)`
`=8mu(1+8lambda)`
So, number is divisible by 8.
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