@article{oai:teapot.lib.ocha.ac.jp:00034602, author = {Hosoya, haruo}, issue = {2}, journal = {お茶の水女子大學自然科學報告}, month = {Feb}, note = {application/pdf, 紀要論文, A Pythagorean triple (PT) composed of a pair of legs, a and b, and hypotenuse, c, is trebly classified and registered by using three differences (Δ, δ, d) among (a b c). Recursive relations among the members of the same group thus classified are extensively studied. These recursive properties are found to be related to the Hall's matrices, U, A, and D, by the operator technique which has been proposed by the present author in 1983. The complicated mathematical structure of PT's under U, A, and D can be greatly simplified by using U^<1/n> and D^<1/n>, which were found to have simple analytical expressions. Further, a number of newly found interesting mathematical properties of PT's are introduced.}, pages = {1--14}, title = {Pythagorean triples. I. Classification and systematization}, volume = {59}, year = {2009} }