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.
For 3 consecutive terms of AP: a-d a & a+d
sum of cubes equals 3*a^3+6a*d^2 and is divisible by 3
so far so good