Bibliographic Details
| Title: |
On the subgroup generated by solutions of Pell's equation. |
| Authors: |
Covill, Elena C.1 ec20covi@siena.edu, Javaheri, Mohammad1 mjavaheri@siena.edu, Krylov, Nikolai A.1 nkrylov@siena.edu |
| Source: |
Journal of Number Theory. Jan2019, Vol. 194, p356-371. 16p. |
| Subjects: |
Mathematical equivalence, Diophantine equations, Integers, Pell's equation, Mathematical models |
| Abstract: |
Abstract Equivalence classes of solutions of the Diophantine equation a 2 + m b 2 = c 2 form an infinitely generated abelian group G m , where m is a fixed square-free positive integer. Solutions of Pell's equation x 2 − m y 2 = 1 generate a subgroup P m of G m. We prove that P m and G m / P m have infinite rank for all m > 1. We also give several examples of m for which G m / P m has nontrivial torsion. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
