All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Probability
Cubic and Consecutive Concern II (Posted on 2010-05-31) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
Rating: 3.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
False start on an analytic solution | Comment 7 of 10 |
n^3 - 1 = (n-1)(n^2+n+1)
(q-a)(q)(q+a) = q(q^2-a^2)

Each is a linear term times a quadratic term so what if the linear terms were equal and the quadratic terms were equal?
q = n-1
q+1=n
Substituting into n^n+n+1 gives the equation
q^2 + 3q + 3 = q^2 - a^2
3q + 3 = -a^2

Unfortunately this has no real solutions for positive q.

It does give plenty of negative solutions though:
(-3)^3 - 1 = -1*-4*-7
(-12)^3 - 1 = -7*-13*-19
etc...


  Posted by Jer on 2010-06-01 15:14:59
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information