Let S
_{i} be the i
^{th} term of an Arithmetic Progression whose 1
^{st} term is a and common difference d. Show that for any 2 positive integers m,n(>m), Σ(i:m to n)(S
_{i})
^{3} can't be a prime number.
Note: a,d are positive integers.
a. the oficial solution asumes even number of members
b. the mean is not nessarily an integer
c The sum of cubes is divisible by the sum of MEMBERS
If no one provides a formal proof within a week -I will do it, despite my laziness
Hint: there are 2 seperate proofs: for m-n being odd or even