On the diophantine equation f ( a m , y ) = b n

Pietro Corvaja; Umberto Zannier

Acta Arithmetica (2000)

  • Volume: 94, Issue: 1, page 25-40
  • ISSN: 0065-1036

How to cite


Corvaja, Pietro, and Zannier, Umberto. "On the diophantine equation $f(a^m,y)=b^n$." Acta Arithmetica 94.1 (2000): 25-40. <http://eudml.org/doc/207423>.

author = {Corvaja, Pietro, Zannier, Umberto},
journal = {Acta Arithmetica},
keywords = {exponential Diophantine equation; infinitely many solutions},
language = {eng},
number = {1},
pages = {25-40},
title = {On the diophantine equation $f(a^m,y)=b^n$},
url = {http://eudml.org/doc/207423},
volume = {94},
year = {2000},

AU - Corvaja, Pietro
AU - Zannier, Umberto
TI - On the diophantine equation $f(a^m,y)=b^n$
JO - Acta Arithmetica
PY - 2000
VL - 94
IS - 1
SP - 25
EP - 40
LA - eng
KW - exponential Diophantine equation; infinitely many solutions
UR - http://eudml.org/doc/207423
ER -


  1. [CZ] P. Corvaja and U. Zannier, Diophantine equations with power sums and universal Hilbert sets, Indag. Math. 9 (1998), 317-332. Zbl0923.11103
  2. [La] S. Lang, Fundamentals of Diophantine Geometry, Springer, 1983. Zbl0528.14013
  3. [Lau] M. Laurent, Équations exponentielles-polynômes et suites récurrentes linéaires, II, J. Number Theory 31 (1989), 24-53. Zbl0661.10027
  4. W. M. Schmidt, Diophantine Approximations and Diophantine Equations, Lecture Notes in Math. 1467, Springer, 1991. Zbl0754.11020
  5. [Se] J.-P. Serre, Lie Algebras and Lie Groups, Lecture Notes in Math. 1500, Springer, 1991. 
  6. [ST] T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge Tracts in Math. 87, Cambridge Univ. Press, 1986. 

Citations in EuDML Documents

  1. Umberto Zannier, Polynomial squares of the form a X m + b ( 1 - X ) n + c
  2. Pietro Corvaja, Umberto Zannier, On the greatest prime factor of Markov pairs
  3. Umberto Zannier, Diophantine equations with linear recurrences An overview of some recent progress
  4. Pietro Corvaja, Umberto Zannier, Finiteness of odd perfect powers with four nonzero binary digits
  5. Dominik J. Leitner, Two exponential diophantine equations
  6. Pietro Corvaja, Umberto Zannier, S-unit points on analytic hypersurfaces

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