A note on the diophantine equation ( x m - 1 ) / ( x - 1 ) = y n

Maohua Le

Acta Arithmetica (1993)

  • Volume: 64, Issue: 1, page 19-28
  • ISSN: 0065-1036

How to cite

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Maohua Le. "A note on the diophantine equation $(x^m-1)/(x-1) = y^n$." Acta Arithmetica 64.1 (1993): 19-28. <http://eudml.org/doc/206531>.

@article{MaohuaLe1993,
author = {Maohua Le},
journal = {Acta Arithmetica},
keywords = {exponential diophantine equation},
language = {eng},
number = {1},
pages = {19-28},
title = {A note on the diophantine equation $(x^m-1)/(x-1) = y^n$},
url = {http://eudml.org/doc/206531},
volume = {64},
year = {1993},
}

TY - JOUR
AU - Maohua Le
TI - A note on the diophantine equation $(x^m-1)/(x-1) = y^n$
JO - Acta Arithmetica
PY - 1993
VL - 64
IS - 1
SP - 19
EP - 28
LA - eng
KW - exponential diophantine equation
UR - http://eudml.org/doc/206531
ER -

References

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  1. [1] A. Baker, The theory of linear forms in logarithms, in: Transcendence Theory: Advances and Applications, Academic Press, London 1977, 1-27. 
  2. [2] D. Estes, R. Guralnick, M. Schacher and E. Straus, Equations in prime powers, Pacific J. Math. 118 (1985), 359-367. Zbl0581.20009
  3. [3] W. Feit, Some consequences of classification of finite simple groups, in: Proc. Sympos. Pure Math. 37, Amer. Math. Soc., 1980, 175-181. Zbl0454.20014
  4. [4] R. Guralnick, Subgroups including the same permutation representation, J. Algebra 81 (1983), 312-319. Zbl0527.20005
  5. [5] L.-K. Hua, Introduction to Number Theory, Springer, Berlin 1982. 
  6. [6] W. Ljunggren, Noen setninger om ubestemte likninger av formen ( x n - 1 ) / ( x - 1 ) = y q , Norsk Mat. Tidsskr. 25 (1943), 17-20. 
  7. [7] R. Perlis, On the class number of arithmetically equivalent fields, J. Number Theory 10 (1978), 489-509. Zbl0393.12009
  8. [8] T. Shorey and R. Tijdeman, New applications of diophantine approximations to diophantine equations, Math. Scand. 39 (1976), 5-18. Zbl0341.10017
  9. [9] C. L. Siegel, Einige Erläuterungen zu Thues Untersuchungen über Annäherungswerte algebraischer Zahlen und diophantische Gleichungen, Nachr. Göttingen Math.-Phys. Kl. II 1970 (8), 169-195. Zbl0215.34601
  10. [10] J. Turk, On the difference between perfect powers, Acta Arith. 45 (1986), 289-307 Zbl0587.10010

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