Is the function $\mathbb{Z}_7 \to \mathbb{Z}_7: x \mapsto x^3 \pmod 7$ a one–one correspondence? And if so, what is the inverse function?
2026-04-03 03:04:52.1775185492
Inverse of arithmetic functions
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You write out the entire table for how this function acts. It won't take long.
Here, I'll start it for you.
$\begin{array}{|c|c|}\hline x&x^3\\\hline 0&0\\\hline 1&1\\\hline 2&?\\\hline 3&6\\\hline 4&?\\\hline 5&?\\\hline 6&?\\\hline \end{array}$