Find the remainder when 22013is divided by 17.

Hi,

Wirte 2²⁰¹³ as 2(17-1)⁵⁰³
Now write the binomial expansion of this term, you will see that the last term containing 17⁰ is the suspicious term. Rest all will be divisible as they have powers of 17.
But if this term is negetive, look at the second last term.

Combine thoes two terms numerically and divide by 17 and then analyze the remainder.
Dont forget to take the 2 written outside the expanison.