1983 AHSME Problems/Problem 14
The units digit of is
First, we notice that is congruent to , is , is , is , is , and so on. This turns out to be a cycle repeating every terms, so is congruent to .
The number has a similar cycle, going Hence we have that is congruent to . Finally, is congruent to . Thus the required units digit is , so the answer is .