What is the easiest way to work out what the last 2 digits are in the expansion 5^2012? without a calculator!
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$5^3 = 125 = 25 = 5^2$ (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.
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