A note on ternary purely exponential diophantine equations

Yongzhong Hu, and Maohua Le. "A note on ternary purely exponential diophantine equations." Acta Arithmetica 171.2 (2015): 173-182. <http://eudml.org/doc/279042>.

@article{YongzhongHu2015,
abstract = {Let a,b,c be fixed coprime positive integers with mina,b,c > 1, and let m = maxa,b,c. Using the Gel’fond-Baker method, we prove that all positive integer solutions (x,y,z) of the equation $a^x+b^y = c^z$ satisfy maxx,y,z < 155000(log m)³. Moreover, using that result, we prove that if a,b,c satisfy certain divisibility conditions and m is large enough, then the equation has at most one solution (x,y,z) with minx,y,z > 1.},
author = {Yongzhong Hu, Maohua Le},
journal = {Acta Arithmetica},
keywords = {ternary purely exponential Diophantine equation; upper bound for solutions; counting solutions},
language = {eng},
number = {2},
pages = {173-182},
title = {A note on ternary purely exponential diophantine equations},
url = {http://eudml.org/doc/279042},
volume = {171},
year = {2015},
}

TY - JOUR
AU - Yongzhong Hu
AU - Maohua Le
TI - A note on ternary purely exponential diophantine equations
JO - Acta Arithmetica
PY - 2015
VL - 171
IS - 2
SP - 173
EP - 182
AB - Let a,b,c be fixed coprime positive integers with mina,b,c > 1, and let m = maxa,b,c. Using the Gel’fond-Baker method, we prove that all positive integer solutions (x,y,z) of the equation $a^x+b^y = c^z$ satisfy maxx,y,z < 155000(log m)³. Moreover, using that result, we prove that if a,b,c satisfy certain divisibility conditions and m is large enough, then the equation has at most one solution (x,y,z) with minx,y,z > 1.
LA - eng
KW - ternary purely exponential Diophantine equation; upper bound for solutions; counting solutions
UR - http://eudml.org/doc/279042
ER -