Heron Triangles with Two Fixed Sides

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Abstract:

In this paper, we study the function Ha, b, which associates to every pair of positive integers a and b the number of positive integers c such that the triangle of sides a, b and c is Heron, i.e., it has integral area. In particular, we prove that Hp, q 5 if p and q are primes and that Ha, b 0 for a random choice of positive integers a and b.

Author(s):
Ionascu, Eugen J. ; Luca, Florian ; Stanica, Pantelimon
Author Organization(s):
NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF APPLIED MATHEMATICS
Descriptive Note:
Journal article
Supplementary Note:
Published in the Number Theory Journal, v126 p52-68, 2007.
Pagination:
0022

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution:
Approved For Public Release
Distribution Statement:
Approved For Public Release; Distribution Is Unlimited.

RECORD

Collection: TR
Identifying Numbers
Monitor Series:
NPS-DAM
 Subject Terms
Joint Capability Areas:
JCA_5_Command and Control; JCA_1.2_Force Preparation; JCA_1_Force Support; JCA_8_Building Partnerships
Modernization Areas:
Fully Networked C3
Communities of Interest:
C4I
Descriptor(s):
*TRIANGLES
Field(s)/Group(s):
Numerical Mathematics
Keyword(s):
TWO FIXED SIDES, HERON TRIANGLES, POSITIVE INTEGERS
Report Date:
2006 Oct 08
Creation Date:
2013 Apr 24