- #1

sg001

- 134

- 0

## Homework Statement

find the least positive integer n for which 5[itex]^{n}[/itex] [itex]\equiv[/itex] 1 (mod17) or 5[itex]^{n}[/itex] [itex]\equiv[/itex] -1 (mod 17)

## Homework Equations

## The Attempt at a Solution

I really don't understand and method to doing these problems as I can't use a calculator and I can only work out powers maybe up to 4 or 5 (depending) in my head... the answer says its 8 but how would I work out in my head 5[itex]^{8}[/itex] +1 and then know it was divisible by 17?

There must be an easier way,,, please help!