What is the simplest way to find all possible solutions for $x^e~ \equiv~ 0 ~~(mod~ n)$? What should be the range of the value of $x$?
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The function $f(x)=x^e$ has a range equal to $\mathbb{R}$. So a necessary step is to find all $x$ such that $f(x)$ is equal to an integer. For a given $n$ there will be infinite many solutions. Whether they show some periodicity that allows to express them in a closed type is debatable. May I ask where you found this? – MathematicianByMistake Nov 06 '17 at 18:38
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There is no source to this question. I was just trying to solve problems on modular equations, so I cooked up this question and wondered whether I can find solutions efficiently in some closed form. I know possible solutions are infinite. – chelsea Nov 06 '17 at 18:43