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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)

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Some Thoughts Initial guidance ??? | Comment 2 of 10 |
Well, that's not the most general formal for a geometric progression, which means that the earlier solution outline might be missing solutions.

a, a+b, a+2b is general, 

which means that N^3 - 1 must be a(a^2 +3ab+2b^2).

It might be easier to work with
q-a, q, q+a

which means that N^3 - 1 must be q(q^2 -a^2) where q > a.

  Posted by Steve Herman on 2010-06-01 01:24:43
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