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## Homework Statement

Reduce 3

^{4567}modulo 19.

## Homework Equations

## The Attempt at a Solution

I approached by first reducing 4567 modulo 18.

I got the following: 3

^{4567}= 3

^{18*253+13}=(3

^{18})

^{253}*3

^{13}congruent to 1

^{253}1594323 congruent to 14 mod 19

Is this the correct approach? I am not sure where 14 came from in the end I just guess and checked until I found a value that worked which was 14. Any explanations on how to correctly find 14?