I need a good reference (preferably a textbook in number theory) to the following known result, attributed to Gauss in Wikipedia.

Theorem (Gauss).Let $ p $ to be a prime number, $ k in mathbb N $ and $ mathbb Z_ {p ^ k} ^ times $ to be the multiplicative group of the invertible elements of the residue ring $ mathbb Z_ {p ^ k}: = mathbb Z / p ^ k mathbb Z $.

Yes $ p $ is strange, then the group $ mathbb Z_ {p ^ k} ^ times $ is cyclical.

Yes $ p = $ 2 and $ k $ 3then the element $ -1 + 2 ^ k mathbb Z $ generates a $ 2 $subgroup $ C_2 subset mathbb Z_ {2 ^ k} ^ times $ and the element $ 5 + 2 ^ k mathbb Z $ generates a cyclic subgroup $ C_ {2 ^ {k-2}} subset mathbb Z_ {2 ^ k} ^ times $ control $ 2 ^ {k-2} $ such as $ mathbb Z_ {p ^ k} ^ times = C_2 oplus C_ {2 ^ {k-2}} $.

Please help!