i want to show that $2^{70}\equiv 10 \pmod{13}$ using Fermat's little theorem. I see that $2^{12}\equiv 1 \pmod{13}$ hence $2^{60}\equiv 1 \pmod{13}$ so $2^{70}\equiv 2^{10} \pmod{13}$ but i don't see how to finish this without evaluating $2^{10}$.
using Fermat's little theorem to reduce a large number mod a prime
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elementary-number-theory