1.start from multiplicative group modulus N where N is odd. 2.take all elements of subgroup with generator equal 2.
question : what do you need to know about N (factorization,phi) for fast calculation of total sum of all subgroup elements.
known facts : it is easy to prove , it equal to K*N
it is somehow related to phi(N)
related problems : number of odd elements, number of elements less than (N-1)/2.0 difference between number of odd and even elements - in most cases is not 0.
how calculate K?
example : 35 1,2,4,8,16,32,29,23,11,22,9,18 = 175 = 5*35 even : 7,odd : 5 , 7-5=2
is it related somehow to modular functions(forms)?
fast : O(log n) or something similar ,O(phi(n)) Is very slow.