Find the remainder when 5^99 is divided by 13.
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By Fermats little $\displaystyle 5^{12} \equiv 1 \pmod {13}$ so $\displaystyle 5^{99}=5^{12 \cdot 8}\cdot 5^{3} \equiv 5^3 \pmod{13}$ It's left to find the rest for $\displaystyle 5^3$ when it's divided by 13 and I leave this to you.
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