On equations \((-1)^\alpha p^x+ (-1)^\beta (2^k(2p + 1))^y= z^2\) with Sophie Germain prime \(p\)

DOI10.2140/INVOLVE.2024.17.503zbMATH Open1548.11066MaRDI QIDQ6596274

Yuan Li, Baoxing Liu, Jing Zhang

Publication date: 2 September 2024

Published in: Involve (Search for Journal in Brave)

zbMATH Keywords

exponential Diophantine equationquadratic reciprocity lawLegendre symbolCatalan equationNagell-Ljunggren equationSophie Germain prime

Mathematics Subject Classification ID

Elliptic curves (14H52) Exponential Diophantine equations (11D61) Power residues, reciprocity (11A15)

Cites Work

• On the Diophantine equation \({x^ n-1\over x-1}=y^ q\).
• Generating safe primes
• On the Nagell-Ljunggren equation $(x^n - 1)/(x - 1) = y^q$
• On the diophantine equation $x^2 + b^y = c^z$
• The Diophantine equation $x^2 + q^m =p^n$
• Primary cyclotomic units and a proof of Catalans conjecture
• A note on the diophantine equation $x² + b^y = c^z$
• On the diophantine equation $(x^m-1)/(x-1) = y^n$
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