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dc.contributor.authorStănică, Pantelimon
dc.contributor.authorSarkar, Santanu
dc.contributor.authorGupta, Sourav Sen
dc.contributor.authorMaitra, Subhamoy
dc.contributor.authorKar, Nirupam
dc.date2013-01-25
dc.date.accessioned2014-02-18T23:35:49Z
dc.date.available2014-02-18T23:35:49Z
dc.date.issued2013
dc.identifier.citationIntegers 13 (2013), #A3.
dc.identifier.urihttp://hdl.handle.net/10945/38838
dc.description.abstractHeron 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 Ionescu, Luca and Stanica for the general situation of fixed sides a,b. In the case of primes sides p,q, there is an additional hypothesis which helps us to drop the upper bounds on H (p.q). In particular, we prove that H(p,q) is less than or equal to 1 when p - q = 2 (mod 4). We also provide a count for the number of Heron triangles with a fixed height (there exists only one such when the height is prime. Moreover, we study the decomposability property of a Heron triangle into two similar ones, and provide some cases when a Heron triangle is not decomposable.en_US
dc.rightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.en_US
dc.titleCounting Heron triangles with constraintsen_US
dc.contributor.corporateNaval Postgraduate School (U.S.)
dc.contributor.departmentApplied Mathematics


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