On \(p^x-q^y=c\) and related three term exponential Diophantine equations with prime bases.

DOI10.1016/j.jnt.2003.11.008zbMath1080.11032OpenAlexW2053347078WikidataQ56226408 ScholiaQ56226408MaRDI QIDQ1429806

Robert Styer, Reese Scott

Publication date: 27 May 2004

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2003.11.008

zbMATH Keywords

exponential Diophantine equationsWieferich primes

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61)

Related Items (16)

Differences of Harmonic Numbers and the $abc$-Conjecture ⋮ On the generalized Pillai equation \(\pm a^{x}\pm b^{y}=c\) ⋮ A note on the number of solutions of the Pillai type equation \(| a^x - b^y | = k\) ⋮ Exceptional cases of Terai's conjecture on Diophantine equations ⋮ ON A CONJECTURE CONCERNING THE NUMBER OF SOLUTIONS TO ⋮ The number of solutions to the generalized Pillai equation \(\pm ra^{x} \pm sb^{y}=c\). ⋮ Jeśmanowicz' conjecture on exponential Diophantine equations ⋮ On the Diophantine equation \(p^{x_1} - p^{x_2} = q^{y_1} - q^{y_2}\) ⋮ Unnamed Item ⋮ Number of solutions to \(ka^x+lb^y=c^z\) ⋮ The generalized Pillai equation \(\pm ra^x\pm sb^y=c\) ⋮ On a remark of Makowski about perfect numbers ⋮ Unnamed Item ⋮ RECOGNITION OF SOME FINITE SIMPLE GROUPS OF TYPE D_n(q) BY SPECTRUM ⋮ A note on the exponential Diophantine equation (A^2n)^x+(B^2n)^y=((A^2+B^2)n)^z ⋮ A note on Jeśmanowicz' conjecture concerning primitive Pythagorean triples

Cites Work

• Solving exponential diophantine equations using lattice basis reduction algorithms
• On the equations \(p^x - b^y = c\) and \(a^x + b^y = c^z\)
• Sur une classe d'équations exponentielles
• Exponential diophantine equations with four terms
• The diophantine equation \(x^ 2 + 2^ k = y^ n\)
• On Cohn's conjecture concerning the Diophantine equation \(x^2+2^m=y^n\)
• On the diophantine equation \(x^ 2+2^ k=y^ n\)
• The Diophantine equation \(x^2+2^k=y^n\). II
• On the equation \(x^2 + 2^a \cdot 3^b = y^n\)
• Existence of primitive divisors of Lucas and Lehmer numbers
• On Some Exponential Equations of S. S. Pillai
• The Solution of y 2 ± 2 n = x 3
• A corollary to a theorem of Laurent-Mignotte-Nesterenko
• Class number bounds and Catalan’s equation
• Ternary Diophantine Equations via Galois Representations and Modular Forms
• Applications of a lower bound for linear forms in two logarithms to exponential Diophantine equations
• Small Two-Variable Exponential Diophantine Equations
• On the Equation a x - b y = 1
• On the Equation a x - b y = 1
• Exponential diophantine equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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