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.

Submitted by K Sengupta

Rating: 4.0000 (3 votes)

Solution: (Hide)

The required probability is 0.04.
For an explanation, refer to the solution submitted by Brian Smith in this location.
Also note the respective rejoinders by Brian Smith and broll here and here.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: Infinite family of solutions - Solution not in the family	Brian Smith	2010-06-04 19:58:53
re: Infinite family of solutions	broll	2010-06-02 10:03:22
Infinite family of solutions	Brian Smith	2010-06-01 20:21:58
False start on an analytic solution	Jer	2010-06-01 15:14:59
re: analytical solution?	Ady TZIDON	2010-06-01 09:23:47
analytical solution?	broll	2010-06-01 07:21:59
re: Initial guidance ???	Ady TZIDON	2010-06-01 04:44:27
Program Solution	Brian Smith	2010-06-01 01:38:21
Initial guidance ???	Steve Herman	2010-06-01 01:24:43
INITIAL GUIDANCE	Ady TZIDON	2010-06-01 00:09:43

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