A note on perfect powers of the form x m - 1 + . . . + x + 1

Maohua Le

Acta Arithmetica (1995)

  • Volume: 69, Issue: 1, page 91-98
  • ISSN: 0065-1036

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Maohua Le. "A note on perfect powers of the form $x^{m-1} + ... + x + 1$." Acta Arithmetica 69.1 (1995): 91-98. <http://eudml.org/doc/206674>.

@article{MaohuaLe1995,
author = {Maohua Le},
journal = {Acta Arithmetica},
keywords = {perfect powers; exponential diophantine equations},
language = {eng},
number = {1},
pages = {91-98},
title = {A note on perfect powers of the form $x^\{m-1\} + ... + x + 1$},
url = {http://eudml.org/doc/206674},
volume = {69},
year = {1995},
}

TY - JOUR
AU - Maohua Le
TI - A note on perfect powers of the form $x^{m-1} + ... + x + 1$
JO - Acta Arithmetica
PY - 1995
VL - 69
IS - 1
SP - 91
EP - 98
LA - eng
KW - perfect powers; exponential diophantine equations
UR - http://eudml.org/doc/206674
ER -

References

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  1. [1] M. Aaltonen and K. Inkeri, Catalan’s equation x p - y q = 1 and related congruences, Math. Comp. 56 (1991), 359-370. 
  2. [2] A. Baker, Rational approximations to ∛2 and other algebraic numbers, Quart. J. Math. Oxford 15 (1964), 375-383. Zbl0222.10036
  3. [3] W. F. H. Berwick, Integral Bases, Cambridge Univ. Press, 1927. Zbl53.0142.01
  4. [4] J. W. S. Cassels, On the equation a x - b y = 1 , II, Math. Proc. Cambridge Philos. Soc. 56 (1960), 97-103. Zbl0094.25702
  5. [5] L.-K. Hua, Introduction to Number Theory, Springer, Berlin, 1982. 
  6. [6] S. Lang, Algebraic Number Theory, Addison-Wesley, Reading, Massachusetts, 1970. Zbl0211.38404
  7. [7] M.-H. Le, A note on the equation ( x m - 1 ) / ( x - 1 ) = y n + 1 , Math. Proc. Cambridge Philos. Soc. 115 (1994), to appear. 
  8. [8] W. Ljunggren, Noen setninger om ubestemte likninger av formen ( x n - 1 ) / ( x - 1 ) = y q , Norsk Mat. Tidsskr. 25 (1943), 17-20. 
  9. [9] W. Ljunggren, On an improvement of a theorem of T. Nagell concerning the diophantine equation Ax³ + By³ = C, Math. Scand. 1 (1953), 297-309. Zbl0051.27803
  10. [10] T. N. Shorey, Perfect powers in values of certain polynomials at integer points, Math. Proc. Cambridge Philos. Soc. 99 (1986), 195-207. Zbl0598.10029
  11. [11] T. N. Shorey, On the equation z q = ( x n - 1 ) / ( x - 1 ) , Indag. Math. 48 (1986), 345-351. Zbl0603.10018
  12. [12] C. L. Siegel, Die Gleichung a x n - b y n = c , Math. Ann. 144 (1937), 57-68. 

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