How can we prove that $19^{20}\equiv 1 \mod 181$?
finding a method to prove that $19^{20}\equiv 1 \mod 181$
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elementary-number-theory
modular-arithmetic
1 Answers
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$$19^2\equiv 361 \equiv -1 \pmod{181}\implies 19^{20}\equiv (19^2)^{10}\equiv(-1)^{10} \equiv 1 \pmod{181}$$