# 1983 AHSME Problems/Problem 14

Revision as of 22:24, 19 March 2017 by Crocodile 40 (talk | contribs) (Created page with "First, we notice that <math>3^0</math> is congruent to <math>1</math> (mod 10), <math>3^1</math> is <math>3</math> (mod 10), <math>3^2</math> is <math>9</math> (mod 10), <math...")

First, we notice that is congruent to (mod 10), is (mod 10), is (mod 10), is (mod 10), is (mod 10), and so on.... This turns out to be a cycle repeating every 4 powers.

Then, we have is congruent to (mod 10).

The number has a similar cycle, going: . Following that, we have is congruent to (mod 10).

is congruent to (mod 10) = .

is congruent to (mod 10).