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 P: 4 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 (p-1) 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’s-Totient function of A.