find all incongruent integers having order 4 modulo 37

Nov 9th 2008, 10:00 AM

ThePerfectHacker

Quote:

Originally Posted by mndi1105

find all incongruent integers having order 4 modulo 37

Notice that $\displaystyle 2$ is a primitive root. Therefore, $\displaystyle 2^{(37-1)/4} = 2^9$ has order $\displaystyle 4$. But that means $\displaystyle 2^9, (2^9)^3$ all have order 4.