Hi. solve simultaneously: x^2=a^2 x^5=e (e is the identity element in G) Um... x=a^(5k) k in the positive integers? Easy guys, I'm a beginner. Thanks.
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is the idea that we have to solve for x in terms of a? if so, then e = x^5 = (x^2)(x^2)x = (a^2)(a^2)x = (a^4)x so therefore: (a^-4) = (a^-4)e = (a^-4)(a^4x) = (a^-4a^4)x = ex = x.
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