What is the remainder when \(17^{200}\) is divided by 18?
Answer: A
We can use the remainder theorem. \(17\) can be written as \((18 - 1)\). So, we need to find the remainder of \((18-1)^{200} \div 18\).
Using the binomial expansion, every term except the last one will have 18 as a factor. The last term is \((-1)^{200}\).
\((-1)^{200} = 1\).
So the remainder is 1.