Problem
NT-B1-M10-P018 Period of \(\frac{1}{27}\)
#18
★★★☆☆ Level 3 of 5
Find the period length of \(\frac{1}{27}\).
Find the order of \(10\) modulo \(27\).
We have \(10^1\equiv10\), \(10^2\equiv100\equiv19\), \(10^3\equiv190\equiv1\pmod{27}\). Smaller positive powers do not give \(1\), so the period is \(3\).
Good example where the modulus is not prime.