perplexus.info :: Probability : Cubic and Consecutive Concern II

Cubic and Consecutive Concern II (Posted on 2010-05-31)

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.

See The Solution Submitted by K Sengupta

Rating: 4.0000 (3 votes)

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re: Initial guidance ???

| Comment 4 of 10 |

(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.

Posted by Ady TZIDON on 2010-06-01 04:44:27

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