On Diophantine Equations 2x ± (2kp)y = z2 and −2x + (2k3)y = z2

In this paper, we solve three Diophantine equations: 2x±(2kp)y=z2 and −2x+(2k3)y=z2 with k≥0 and prime p≡±3(mod8). We obtain all the non-negative integer solutions by using elementary methods and the database of elliptic curves in “The L-functions and modular forms database” (LMFDB).

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Publication Details

Journal
Mathematics
Published
2024-12-22
DOI
https://doi.org/10.3390/math12244027
Primary Topic
Algebraic Geometry and Number Theory
Type
article
Field-Weighted Citation Impact
0.00
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article

On Diophantine Equations 2x ± (2kp)y = z2 and −2x + (2k3)y = z2

Yuan Li, Torre Lloyd, Angel Clinton
1 links
Mathematics
Algebraic Geometry and Number Theory
article

On Diophantine Equations 2x ± (2kp)y = z2 and −2x + (2k3)y = z2

Yuan Li, Torre Lloyd, Angel Clinton
article en

Abstract

In this paper, we solve three Diophantine equations: 2x±(2kp)y=z2 and −2x+(2k3)y=z2 with k≥0 and prime p≡±3(mod8). We obtain all the non-negative integer solutions by using elementary methods and the database of elliptic curves in “The L-functions and modular forms database” (LMFDB).

MathematicsVol. 12(24)
Winston-Salem State University (US)
Openalex Percentile: Top 63%
Algebraic Geometry and Number Theory
DOIOpen Access PDFOpenAlex
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On Diophantine Equations 2x ± (2kp)y = z2 and −2x + (2k3)y = z2 — Yuan Li, Torre Lloyd, et al. · Mathematics (2024) | TGRS Research Map | TGRS