Question

Find the remainder when
2^1000
is divisible by 17​

Answer 1

Answer:

This is a question in modular arithmetic.

Note that 2^4 = 16, and 16 == -1 mod 17.

Now 2^1000 = 16^250 == (-1)^250 mod 17 = 1 mod 17

So the remainder when 2^1000 is divided by 17 is 1.