I want to submit a paper on proof of this formula, so can some one please tell whether this already exists or not?
Let S’(A) be the set of elements in GF(p) such that S’(A) = {x/ O(x,p) = A}. Here A should be
the factor of (p1) and A>2, where p is prime, then
∑x = μ(A) + ½* T(A)*p;
where the summation is over all the elements of set S’(A) and
O(x,p) : Order of x with respect to p, (by order it is meant to be multiplicative order).
μ(A) : Mobius function of A.
T(A) : Euler’sTotient function of A.
