Determine the probability that for a positive base ten integer N drawn at random between 2 and 201 inclusively, the number N³ - 1 is expressible in the form p*q*r, where p, q and r are three distinct positive integers such that p, q and r (in this order) corresponds to three consecutive terms of an arithmetic progression.

The number n^3-1 must be of the form a^3 *b *(2*b-1) to enable
the sequence a,a(1+b),a(1+2*b)
  e.g.  a=2 b=6   gives us 8*7*13=728=3^9-1

and the 1st solution is 2,14,26  and  if n  were limited to first 9 integers  the  requested probability would be 1/9.

 

To continue- Write a program to find what pairs (a,b) create n^3-1:.
range until  reaching 202^3.
-Then calculate probability

Edited on June 1, 2010, 12:42 am

Posted by Ady TZIDON on 2010-06-01 00:09:43