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

Posted by Ady TZIDON on 2008-03-06 12:42:29