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Groups and FieldsEasyPermutation Groups

Permutation Groups · Easy problem

In Z9\mathbb{Z}_9 under addition mod 99, the regular representation sends 44 to the permutation λ4 ⁣:x↦x+4(mod9)\lambda_4\colon x \mapsto x+4 \pmod 9. Find the x∈{0,…,8}x \in \{0,\ldots,8\} with λ4(x)=7\lambda_4(x) = 7.