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.

(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