(1) Show that if n is an integer which has primitive roots, then the product of the integers less than or equal to n and relatively prime to n == -1(mod n).
(2) Show that (1) is not true if n does not have a primitive root.
(1) Show that if n is an integer which has primitive roots, then the product of the integers less than or equal to n and relatively prime to n == -1(mod n).
(2) Show that (1) is not true if n does not have a primitive root.
The demonstration is an if and only if one, so both directions are already contained in it....what part you didn't get? That there's a primitive root w of n means that all the units in , i.e. the elements of , i.e. all the integers modulo n which are coprime to n, are a power of w <==> the group is cyclic of order ...in the last equality I used that is even for any ...
Tonio