Heron triangles with two fixed sides
نویسندگان
چکیده
منابع مشابه
A ug 2 00 6 Heron triangles with two fixed sides
In this paper, we study the function H(a, 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., has integral area. In particular, we prove that H(p, q) ≤ 5 if p and q are primes, and that H(a, b) = 0 for a random choice of positive integers a and b.
متن کاملCounting Heron Triangles with Constraints
Heron triangles have the property that all three of their sides as well as their area are positive integers. In this paper, we give some estimates for the number of Heron triangles with two of their sides fixed. We provide a general bound on this count H(a, b), where the sides a, b are fixed positive integers, and the estimate here is better than the one of Ionascu, Luca and Stănică for the gen...
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There has previously been given a one-parameter family of pairs of Heron triangles with equal perimeter and area. In this note, we find two twoparameter families of such triangle pairs, one of which contains the known one-parameter family as a special case. Second, for an arbitrary integer n > 2 we show how to find a set of n Heron triangles in two parameters such that all triangles have equal ...
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A Heron triangle is a triangle having the property that the lengths of its sides as well as its area are positive integers. Let P be a fixed set of primes, let S denote the set of integers divisible only by primes in P. We prove that there are only finitely many Heron triangles whose sides a, b, c ∈ S and are reduced, that is gcd(a, b, c) = 1. If P contains only one prime ≡ 1 (mod 4) then all t...
متن کامل# a 3 Integers 13 ( 2013 ) Counting Heron Triangles with Constraints
Heron triangles have the property that all three of their sides as well as their area are positive integers. In this paper, we give some estimates for the number of Heron triangles with two of their sides fixed. We provide a general bound on this count H(a, b), where the sides a, b are fixed positive integers, and the estimate here is better than the one of Ionascu, Luca and Stănică for the gen...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2007
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2006.12.004