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Groups and FieldsEasyCosets and Lagrange's Theorem

Cosets and Lagrange's Theorem · Easy problem

In U(16)={1,3,5,7,9,11,13,15}U(16)=\{1,3,5,7,9,11,13,15\}, the element 77 satisfies 72≡1(mod16)7^2\equiv1\pmod{16}, so ord⁡(7)=2\operatorname{ord}(7)=2. Using this, find 711 mod 167^{11}\bmod16.