MathCastle
Groups and FieldsChallengeGroups and the Group Axioms

Groups and the Group Axioms · Challenge problem

Suppose a,xa,x are elements of a group with x∗a∗x−1=a−1x*a*x^{-1}=a^{-1}. Find the integer nn with 0≤n<50\le n<5 such that x7∗a∗x−7=anx^7*a*x^{-7}=a^n, given also a5=ea^5=e.