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Consecutive 8-Digit Heron (Posted on 2009-11-15) Difficulty: 3 of 5
The side lengths of a Heronian Triangle are R-1, R and R+1, where R is an 8-digit positive integer which does not contain any leading zero.

Determine all possible value(s) of R for which this is possible.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: One possible value | Comment 2 of 4 |
(In reply to One possible value by Jim Keneipp)

I am fairly sure the recursion you gave generates all solutions.  The equation R^2 - 4 = 3N^2 is a Pell-like equation.  Those typically have only one family of solutions related by recursion.  I usually find the recursion formula and leave it at that.
  Posted by Brian Smith on 2009-11-16 13:04:47

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