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2003 A Remark on Prim Divisors of Lengths of Sides of Heron Triangles
István Gaál, István Járási, Florian Luca
Experiment. Math. 12(3): 303-310 (2003).


A Heron triangle is a triangle having the property that the lengths of its sides as well as its area are positive integers. Let {\small ${\cal P}$} be a fixed set of primes; let S denote the set of integers divisible only by primes in {\small ${\cal P}$}. We prove that there are only finitely many Heron triangles whose sides {\small $a,b,c\in S$} and are reduced, that is {\small $\gcd (a,b,c)=1$}. If {\small ${\cal P}$} contains only one prime {\small $\equiv 1\; (\bmod \; 4)$}, then all these triangles can be effectively determined. In case {\small ${\cal P}=\{2,3,5,7,11\}$}, all such triangles are explicitly given.


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István Gaál. István Járási. Florian Luca. "A Remark on Prim Divisors of Lengths of Sides of Heron Triangles." Experiment. Math. 12 (3) 303 - 310, 2003.


Published: 2003
First available in Project Euclid: 15 June 2004

zbMATH: 1096.11011
MathSciNet: MR2034394

Primary: 11D57 , 11Y50

Keywords: Heron triangle , reduction , S-unit equation

Rights: Copyright © 2003 A K Peters, Ltd.


Vol.12 • No. 3 • 2003
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