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.

The official  solution asumes even number of members

It is easy to show that the sum of cubes is always divisible by the mean,  m-n being odd or even,

b. 

Edited on January 19, 2021, 3:11 am

Posted by Ady TZIDON on 2008-03-08 19:45:10