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Groups and Distinct Elements

Let G be a group and let be two distinct elements. Let n be the order of g and m be the order of h. Prove or disprove that there is no pair i,j , such that .

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Let G= , x*y be the fractional part of x+y .(i.e:x*y=x+y-[x+y] where
[a] is the greatest integer less than or equal than ...

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