Divisor of Integer/Examples/6 divides 7^n - 1/Proof 2
Jump to navigation
Jump to search
Theorem
Let $n \in \Z_{\ge 0}$ be a positive integer.
Then:
- $6 \divides 7^n - 1$
where $\divides$ denotes divisibility.
Proof
From Integer Less One divides Power Less One, we have that:
- $\forall m, n \in \Z: \paren {m - 1} \divides \paren {m^n - 1}$
This result is the special case where $m = 7$.
$\blacksquare$