Find the order of each element in U(36), the group of units modulo 36

Find all possible positive values of m: 47 = m mod (5)

For each divisor k . 1 of n, let Uk(n) = {x ∈ U(n) | x mod k = 1}. [For example, U3(21) = {1, 4, 10, 13, 16, 19} and U7(21) = {1, 8}.] List the elements of U4(20), U=(20), U=(30), and U10(30). Prove that Uk(n) is a subgroup of U(n). Let H = {x [ U(10) | x mod 3 = 1}. Is H a subgroup of U(10)? (This exercise is referred to in Chapter 8.)

. (a) If g is a primitive root modulo 37, which of the numbers g², g³,..., g8 are primitive roots modulo 37?