Here is one problem idea that I have. I do have a slight feeling that this might be a very standard or direct question. Please give feed back or suggestions to improve the question.
Here is the basic statement.
Given an array of 10^5 positive numbers ( each no. <= 10^5 ). and 10^5 queries of the form M L R.
aL%M + a(L+1)%M … aR%M.