1983 AHSME Problems/Problem 14
Problem
The units digit of is
Solution
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 .
See Also
1983 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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