Pythagorean triangles with legs less than n
Abstract
We obtain asymptotic estimates for the number of Pythagorean triples (a,b,c) such that a<n, b<n. These estimates (considering the triple (a,b,c) different from (b,a,c)) is in the case of primitive triples, and in the case of general triples. Furthermore, we derive, by a self-contained elementary argument, a version of the first formula which is weaker only by a log-factor. Also, we tabulate the number of primitive Pythagorean triples with both legs less than n, for selected values of n[less-than-or-equals, slant]1 000 000 000, showing the excellent precision obtained.
- Publication:
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Journal of Computational and Applied Mathematics
- Pub Date:
- June 2002
- DOI:
- Bibcode:
- 2002JCoAM.143..117B
- Keywords:
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- Pythagorean triples;
- Pythagorean triangles