Question

When $2^{256}$ is divided by 17, the remainder would be : (CAT 2002)

• A. 1
• B. 16
• C. 14
• D. None of these

Answer 1

The correct option is A 1

Ans: (a)

$2^{256}$ can be written as $(2^4{)}^{64}=(17-1{)}^{64}.$

In the expansion of $(17-1{)}^{64}$every term is divisible by $17$ except $(-1{)}^{64}$. Hence remainder is 1.

Or directly:

Euler's number of 17 is 16 and 256 is a multiple of 16, hence the remainder is 1.