I found a weird relationship and was hoping someone could explain why it happens:
In module M, there exists a x not equal to 1, such that x^3=1
If and only if:
3 divides the Euler Totient Phi function of M.
Any insights? (if this is not accurate, please let me know, but this relationship seems to hold true for all modulo bellow 300)
(Sorry if my tagging is bad... don't know enough to properly tag this)