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

 

Posted by Ady TZIDON on 2008-03-03 16:31:20