lean_workbook_plus_62844

Suppose $d \vert n$ , where $d$ and $n$ are positive integers. Write $n = dk$ and let $y = p^d$ . Then the identity $y^k - 1 = (y-1)(y^{k-1} + y^{k-2} + \cdots + 1)$ shows that $p^d - 1$ divides $p^n - 1$ .