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 selfcontained elementary argument, a version of the first formula which is weaker only by a logfactor. Also, we tabulate the number of primitive Pythagorean triples with both legs less than n, for selected values of n[lessthanorequals, slant]1 000 000 000, showing the excellent precision obtained.
 Publication:

Journal of Computational and Applied Mathematics
 Pub Date:
 June 2002
 DOI:
 10.1016/S03770427(01)004964
 Bibcode:
 2002JCoAM.143..117B
 Keywords:

 Pythagorean triples;
 Pythagorean triangles