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.
It is surely true for the sum of the two 1st members: a and a+d,
denote a+d by b:
a^3+b^3=(a+b)*(a^2-ab+b^2) ==> is not prime/
From here I don't know how to follow
Ady