(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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)

2. Relevant equations

3. The attempt at a solution

I really dont understand and method to doing these problems as I cant 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!

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# Homework Help: Least positive integer, modular problem HELP!

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