The question tasks me to find all x such that $2^x \equiv 1 \pmod{7}$.
By inspection I can see that $x \equiv 0 \pmod{3}$ but is there a way to show this using Fermat's little theorem?
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To start off, what does Fermat's little theorem tell you about multiplication $\pmod{7}$? – aschepler Jul 28 '23 at 16:31
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See the Theorem in the linked dupe. – Bill Dubuque Jul 28 '23 at 16:35