How can I calculate $8^{-13}\pmod{29}$ ? I don't get how it works. Can I do it separately? So first $8^{-13}$ and then modulo $29$. And how can I calculate a negative power the quickest?
2026-04-12 07:43:00.1775979780
Calculate inverse modulo: $8^{-13}\pmod {29}$
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HINT:
Using Fermat's Little Theorem, $\displaystyle2^{28}\equiv1\pmod{29},$
$\displaystyle8^{-13}=(2^3)^{-13}=2^{-39}\equiv (2^{28})^{(-2)}\cdot2^{17}\equiv2^{17}\pmod{29}$
Now, observe that $\displaystyle2^5=32\equiv3\pmod{29}$
Can you take it from here?