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Groups and FieldsMediumPermutation Groups

Permutation Groups · Medium problem

In U(7)={1,…,6}U(7) = \{1,\ldots,6\} under multiplication mod 77, the regular representation sends 33 to λ3 ⁣:x↦3x(mod7)\lambda_3\colon x \mapsto 3x \pmod 7. Find the x∈{1,…,6}x \in \{1,\ldots,6\} with λ3(x)=5\lambda_3(x) = 5.