Determine the probability that for a positive base ten integer N drawn at random between 2 and 201 inclusively, the number N^{3} - 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.

(In reply to

Initial guidance ??? by Steve Herman)

You wrote :

."..Well, that's not the most general formal for a **geometric** progression, which means that the earlier solution outline might be missing solutions. "

I understand you have meant **arithmetic.**

**
**

Which shows that everyone can err.

**My error **was assuming(gut feelings,maybe) that the three

members of the ar.prog. cannot be relatively prime, so they share common divisor a.

So a, a+d and a+2d become a*(1, 1+b, 1+2b) and I miss all the

solutions that do not support my assumption.