On the equations \(p^x - b^y = c\) and \(a^x + b^y = c^z\)
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Publication:687512
DOI10.1006/jnth.1993.1041zbMath0786.11020OpenAlexW1979276230MaRDI QIDQ687512
Publication date: 18 October 1993
Published in: Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jnth.1993.1041
Related Items (25)
The diophantine equation \(a^ x+b^ y=c^ z\) ⋮ Differences of Harmonic Numbers and the $abc$-Conjecture ⋮ THE SHUFFLE VARIANT OF JEŚMANOWICZ’ CONJECTURE CONCERNING PYTHAGOREAN TRIPLES ⋮ On the generalized Pillai equation \(\pm a^{x}\pm b^{y}=c\) ⋮ A purely exponential Diophantine equation in three unknowns ⋮ An upper bound for the number of solutions of the exponential diophantine equation \(a^x+b^y=c^z\) ⋮ A note on the diophantine equation \((m^3-3m)^x+(3m^2-1)^y=(m^2+1)^z\) ⋮ A note on the number of solutions of the Pillai type equation \(| a^x - b^y | = k\) ⋮ Generalizations of classical results on Jeśmanowicz' conjecture concerning Pythagorean triples ⋮ 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 \(\pm ra^{x} \pm sb^{y}=c\). ⋮ Unnamed Item ⋮ On the exponential Diophantine equation \((m^2+m+1)^x+m^y=(m+1)^z\) ⋮ Jeśmanowicz' conjecture on exponential Diophantine equations ⋮ On \(p^x-q^y=c\) and related three term exponential Diophantine equations with prime bases. ⋮ Number of solutions to \(ka^x+lb^y=c^z\) ⋮ Unnamed Item ⋮ The generalized Pillai equation \(\pm ra^x\pm sb^y=c\) ⋮ Polynomial cycles in certain rings of rationals ⋮ On the exponential Diophantine equation \(a^x+b^y=c^z\) ⋮ On Erdős-Wood's conjecture ⋮ Pillai's conjecture revisited. ⋮ Bennett's Pillai theorem with fractional bases and negative exponents allowed ⋮ A NOTE ON THE NUMBER OF SOLUTIONS OF TERNARY PURELY EXPONENTIAL DIOPHANTINE EQUATIONS
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