Jiaqi WangBeijing National Day SchoolLide CaiBeijing National Day School
S.-T. Yau High School Science Awarded Papersmathscidoc:1608.35147
Dongrun-Yau Science Award, 2013
Pell equation is an important research object in elementary number theory of indefinite equation. its form is simple, but it is rich in nature. Many number theory problems can be transformed into the problem of Pell equation’s solvability. However, the previous methods in determining the Pell equation’s solvability are sophisticated for calculation, which leads to the lack of efficiency. This paper gives new and more widely used methods to determine the solvability of Pell equation, including several necessary conditions, sufficient conditions and necessary and sufficient conditions.
Pell equation, Solvability, Continued fraction expansion, Periodic