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I have no clue to do this. In addition to solving the problem, is there a good approach to solving these types of problems?

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    What do you denote $k^100$? – 2017-02-18
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    For next time, $\LaTeX$ commands like `^`, `_`, `\sqrt` and so on only applies to the very next symbol unless you enclose it in curly brackets. Thus `1^100` becomes $1^100$, while `1^{100}` becomes $1^{100}$. – 2017-02-18
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    @Arthur, well done - first the fix then the explanation. – 2017-02-18
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    @AndreasCaranti My main reason to be on this site is to try my best to educate. Mostly it's math, but some times it's on how to best use the site itself. – 2017-02-18
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    I agree with your philosophy. More often then not, I also try and fix lacking $\LaTeX$ code in questions from newcomers. – 2017-02-18

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$101$ is prime. Use Fermat's little theorem.