Question

Let U(n)={m∈N|(m, n) =1,m≤ n}. Then U(n) is a group with respect to

multiplication modulo n. Find the orders of <m> for each m∈U(10).

Answer 1

U(10)={1,3,7,9}

1¹mod10=1

<1> has order 1

3⁴mod10=1

<3> has order 4

7⁴mod10=1

<7> has order 4

9²mod10=1

<9> has order 2