Pure powers and power classes in recurrence sequences

Péter Kiss

Mathematica Slovaca (1994)

  • Volume: 44, Issue: 5, page 525-529
  • ISSN: 0139-9918

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Kiss, Péter. "Pure powers and power classes in recurrence sequences." Mathematica Slovaca 44.5 (1994): 525-529. <http://eudml.org/doc/34396>.

@article{Kiss1994,
author = {Kiss, Péter},
journal = {Mathematica Slovaca},
keywords = {linear recurrence sequences; linear forms in logarithms of algebraic numbers; pure powers},
language = {eng},
number = {5},
pages = {525-529},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Pure powers and power classes in recurrence sequences},
url = {http://eudml.org/doc/34396},
volume = {44},
year = {1994},
}

TY - JOUR
AU - Kiss, Péter
TI - Pure powers and power classes in recurrence sequences
JO - Mathematica Slovaca
PY - 1994
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 44
IS - 5
SP - 525
EP - 529
LA - eng
KW - linear recurrence sequences; linear forms in logarithms of algebraic numbers; pure powers
UR - http://eudml.org/doc/34396
ER -

References

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  7. LJUNGGREN W., Zur Theorie der Gleichung x 2 + 1 = D y 4, Avh. Norske Vid Akad. Oslo. 5 (1942). (1942) MR0016375
  8. LONDON J.-FINKELSTEIN R., On Fibonacci and Lucas numbers which are perfect powers, Fibonacci Quart. 7 (1969), 476-481, 487 (Errata ibid 8 (1970), 248). (1969) Zbl0206.05402MR0255482
  9. LONDON J.-FINKELSTEIN R., On Mordell’s Equation y 2 - k = x 3 , Bowling Green University Press, 1973. (1973) 
  10. McDANIEL W. L.-RIBENBOIM P., Squares and double-squares in Lucas sequences, C.R. Math. Rep. Acad. Sci. Canada. 14 (1992), 104-108. (1992) Zbl0771.11012MR1167065
  11. PETHO A., Full cubes in the Fibonacci sequence, Publ. Math. Debrecen. 30 (1983), 117-127. (1983) MR0733078
  12. PETHO A., The Pell sequence contains only trivial perfect powers, In: Sets, Graphs and Numbers. Colloq. Math. Soc. Janos Bolyai 60, North-Holland, Amsterdam-New York, 1991, pp. 561-568. (1991) MR1218218
  13. PETHO A., Perfect powers in second order linear recurrences, J. Number Theory, 15 (1982), 5-13. (1982) MR0666345
  14. PETHO A., Perfect powers in second order recurrences, In: Topics in Classical Number Theory, Akademiai Kiado, Budapest, 1981, pp. 1217-1227. (1981) MR0781182
  15. RIBENBOIM P., Square classes of Fibonacci and Lucas numbers, Portugal. Math. 46 (1989), 159-175. (1989) Zbl0687.10005MR1020964
  16. RIBENBOIM P., McDANIEL W. L., Square classes of Fibonacci and Lucas sequences, Portugal. Math. 48 (1991), 469-473. (1991) MR1147611
  17. RIBENBOIM P., Square classes of ( a n - l ) / ( a - 1 ) and a n + 1 , Sichuan Daxue Xunebar, 26 (1989), 196-199. (1989) MR1059704
  18. ROBBINS N., On Fibonacci numbers of the form P X 2 , where P is prime, Fibonacci Quart. 21 (1983), 266-271. (1983) MR0723787
  19. ROBBINS N., On Pell numbers of the form P X 2 , where P is prime, Fibonacci Quart. 22 (1984), 340-348. (1984) MR0766310
  20. SHOREY T. N., STEWART C. L., On the Diophantine equation a x 2 t + b x t y + c y 2 = d and pure powers in recurrence sequences, Math. Scand. 52 (1983), 24-36. (1983) MR0697495
  21. SHOREY T. N., STEWART C. L., Pure powers in recurrence sequences and some related Diophatine equations, J. Number Theory 27 (1987), 324-352. (1987) MR0915504
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