A Survey on the Ternary Purely Exponential Diophantine Equation $a^x + b^y = c^z$

zbMath1438.11086arXiv1808.06557MaRDI QIDQ5225498

Reese Scott, Maohua Le, Robert Styer

Publication date: 22 July 2019

Full work available at URL: https://arxiv.org/abs/1808.06557

zbMATH Keywords

ternary purely exponential Diophantine equationJeśmanowicz conjectureTerai-Jeśmanowicz conjecture

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61)

Related Items (16)

A purely exponential Diophantine equation in three unknowns ⋮ On the exceptional solutions of Jeśmanowicz' conjecture ⋮ Pillai's equation in polynomials ⋮ A parametric family of ternary purely exponential Diophantine equation $A^x+B^y=C^z$ ⋮ ON A CONJECTURE CONCERNING THE NUMBER OF SOLUTIONS TO ⋮ A note on the ternary purely exponential Diophantine equation \(f^x + (f + g)^y = g^z\) ⋮ Jeśmanowicz' conjecture for non-primitive Pythagorean triples ⋮ On the exponential Diophantine equation \((m^2+m+1)^x+m^y=(m+1)^z\) ⋮ Unnamed Item ⋮ A note on the exceptional solutions of Jeśmanowicz' conjecture concerning primitive Pythagorean triples ⋮ Dem'janenko's theorem on Jeśmanowicz' conjecture concerning Pythagorean triples revisited ⋮ 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 NONPRIMITIVE PYTHAGOREAN TRIPLES ⋮ A note on the exponential Diophantine equation \((rlm^2-1)^x+(r(r-l)m^2+1)^y=(rm)^z\) ⋮ A further note on Jeśmanowicz' conjecture concerning primitive Pythagorean triples ⋮ A NOTE ON THE NUMBER OF SOLUTIONS OF TERNARY PURELY EXPONENTIAL DIOPHANTINE EQUATIONS

This page was built for publication: A Survey on the Ternary Purely Exponential Diophantine Equation $a^x + b^y = c^z$