On the diophantine equation ( x m - 1 ) / ( x - 1 ) = y n

Li Yu; Maohua Le

Acta Arithmetica (1995)

  • Volume: 73, Issue: 4, page 363-366
  • ISSN: 0065-1036

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Li Yu, and Maohua Le. "On the diophantine equation $(x^m-1)/(x-1) = y^n$." Acta Arithmetica 73.4 (1995): 363-366. <http://eudml.org/doc/206826>.

@article{LiYu1995,
author = {Li Yu, Maohua Le},
journal = {Acta Arithmetica},
keywords = {finite simple groups; exponential diophantine equations; Edgar's conjecture},
language = {eng},
number = {4},
pages = {363-366},
title = {On the diophantine equation $(x^m-1)/(x-1) = y^n$},
url = {http://eudml.org/doc/206826},
volume = {73},
year = {1995},
}

TY - JOUR
AU - Li Yu
AU - Maohua Le
TI - On the diophantine equation $(x^m-1)/(x-1) = y^n$
JO - Acta Arithmetica
PY - 1995
VL - 73
IS - 4
SP - 363
EP - 366
LA - eng
KW - finite simple groups; exponential diophantine equations; Edgar's conjecture
UR - http://eudml.org/doc/206826
ER -

References

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  1. [1] H. Edgar, Problems and some results concerning the diophantine equation 1 + A + A ² + . . . + A x - 1 = P y , Rocky Mountain J. Math. 15 (1985), 327-329. Zbl0583.10012
  2. [2] R. K. Guy, Unsolved Problems in Number Theory, Springer, New York, 1981. 
  3. [3] K. Inkeri, On the diophantine equation a ( x m - 1 ) / ( x - 1 ) = y n , Acta Arith. 21 (1972), 299-311. Zbl0228.10017
  4. [4] M.-H. Le, A note on the diophantine equation ( x m - 1 ) / ( x - 1 ) = y n , Acta Arith. 64 (1993), 19-28. 
  5. [5] M.-H. Le, A note on perfect powers of the form x m - 1 + . . . + x + 1 , Acta Arith. 69 (1995), 91-98. Zbl0819.11012
  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. Obláth, Une propriété des puissances parfaites, Mathesis 65 (1956), 356-364. Zbl0072.26503
  8. [8] W.-J. Shi, On K₄ simple groups, Kexue Tongbao 36 (1991), 1281-1283 (in Chinese). 
  9. [9] T. Shorey and R. Tijdeman, New applications of diophantine approximations to diophantine equations, Math. Scand. 39 (1976), 5-18. Zbl0341.10017
  10. [10] T. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge Univ. Press, 1986. 

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