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Groups and FieldsEasyCosets and Lagrange's Theorem

Cosets and Lagrange's Theorem · Easy problem

1919 is prime and gcd⁡(11,19)=1\gcd(11,19)=1, so Fermat gives 1118≡1(mod19)11^{18}\equiv1\pmod{19}. Using this, find 1119 mod 1911^{19}\bmod19.