1. Index numbers

What is the easiest way to work out what the last 2 digits are in the expansion 5^2012? without a calculator!

2. Re: Index numbers

$5^3 = 125 = 25 = 5^2$ (mod $100$).

Use this to show by induction on $n$, that for $n \geq 2$, that $5^n = 25$ (mod $100$).

Hence the last 2 digits are 25.