# IJPAM: Volume 64, No. 4 (2010)

ON THE PERIMETER OF INTEGRAL TRIANGLES

Russell A. Gordon, Jonathan M. Wells
Whitman College
345, Boyer Avenue, Walla Walla, WA 99362, USA
e-mail: gordon@whitman.edu
e-mail: wellsjm@whitman.edu

Abstract.Given a triangle with relatively prime integral sides and a degree angle, let denote the number of such triangles with perimeter less than or equal to . We consider the asymptotic behavior of the function when has the values , , and , and thus extend known results for degree triangles to degree and degree triangles. The paper is written in such a way that readers with a minimal background in number theory can follow the details of the arguments.

Received: November 6, 2010

AMS Subject Classification: 11N37, 11A25

Key Words and Phrases: perimeter, integral triangle, Eisenstein triple, lattice point

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 64
Issue: 4