Find the last three digits of 101^{202} \(\phantom{101^101}\)
101^202 % 10^10==8603030201 - these are the last 10 digits.
101 = 1.01e2 = 101
101^2 = 10201
101^3 = 1030301
101^9 = 1093685272684360901
101^10 = 110462212541120451001
We seem to have a pattern here, based on the pattern the last 3 digits are most likely 201
