NT-B1-M07-P011 Order of Three

Compute powers until \(1\) appears for the first time.

\(3^1\equiv3\), \(3^2\equiv2\), \(3^3\equiv6\), \(3^4\equiv4\), \(3^5\equiv5\), \(3^6\equiv1\pmod7\). Since \(1\) did not appear earlier, the order is \(6\).

Prepares for conditions like \(3^n\equiv1\).