On the Diophantine equations x2 − 47y2 = 1 and y2 − Pz2 = 49

Jianhong Zhao; Lixing Yang

doi:10.1088/1757-899x/382/5/052037

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On the Diophantine equations x² − 47y² = 1 and y² − Pz² = 49

Jianhong Zhao Lixing Yang

Year: 2018 Journal: IOP Conference Series Materials Science and Engineering Vol: 382 Pages: 052037-052037 Publisher: IOP Publishing

DOI: 10.1088/1757-899x/382/5/052037

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Abstract

The integer solution of diophantine equations x2 − D1y2 = m, (D1 ∈ Z+, m ∈ Z) and y2 − D2z2 = n, (D2 ∈ Z+, n ∈ Z) is a matter of great concern. Researchers study for different m, n and D1, D2, and obtained some correlation results as follows.

Keywords:

Diophantine equation Integer (computer science) Mathematics Diophantine set Applied mathematics Discrete mathematics Pure mathematics Computer science

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On the Diophantine equations x² − 47y² = 1 and y² − Pz² = 49

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