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.
(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.