Question

what are the last three digits of 19^19? Hint use the binomial theorem for [20-1]^19..not sure how to go on..

Answer 1

\[\Large (a+b)^n=\sum_{i=0}^n \left(\begin{matrix}n \\ i\end{matrix}\right)a^{n-i}b^i\]
So maybe you want to play around with this expression a little according to your hint.

Answer 2

i dont think this woud solve the problem