On the divisors of a k + b k

Pieter Moree

Acta Arithmetica (1997)

  • Volume: 80, Issue: 3, page 197-212
  • ISSN: 0065-1036

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Pieter Moree. "On the divisors of $a^k + b^k$." Acta Arithmetica 80.3 (1997): 197-212. <http://eudml.org/doc/207037>.

@article{PieterMoree1997,
author = {Pieter Moree},
journal = {Acta Arithmetica},
keywords = {bad integers; counting function; stufe of a field; good odd prime powers; prime divisors; asymptotic formula},
language = {eng},
number = {3},
pages = {197-212},
title = {On the divisors of $a^k + b^k$},
url = {http://eudml.org/doc/207037},
volume = {80},
year = {1997},
}

TY - JOUR
AU - Pieter Moree
TI - On the divisors of $a^k + b^k$
JO - Acta Arithmetica
PY - 1997
VL - 80
IS - 3
SP - 197
EP - 212
LA - eng
KW - bad integers; counting function; stufe of a field; good odd prime powers; prime divisors; asymptotic formula
UR - http://eudml.org/doc/207037
ER -

References

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  1. [1] C. Ballot, Density of prime divisors of linear recurrences, Mem. Amer. Math. Soc. 551, 1995. 
  2. [2] A. Brauer, A note on a number theoretical paper of Sierpi/nski, Proc. Amer. Math. Soc. 11 (1960), 406-409. Zbl0096.02603
  3. [3] P. Chowla, On the representation of -1 as a sum of squares in a cyclotomic field, J. Number Theory 1 (1969), 208-210. Zbl0177.07401
  4. [4] P. Chowla and S. Chowla, Determination of the Stufe of certain cyclotomic fields, ibid. 2 (1970), 271-272. 
  5. [5] B. Fein, B. Gordon and J. H. Smith, On the representation of -1 as a sum of two squares in an algebraic number field, ibid. 3 (1971), 310-315. Zbl0226.12003
  6. [6] H. Halberstam, unpublished manuscript, 1995. 
  7. [7] H. Hasse, Über die Dichte der Primzahlen p, für die eine vorgegebene ganzrationale Zahl a ≠ 0 von gerader bzw. ungerader Ordnung mod. p ist, Math. Ann. 166 (1966), 19-23. Zbl0139.27501
  8. [8] E. V. Krishnamurthy, An observation concerning the decimal periods of prime reciprocals, J. Recreational Math. 24 (1969), 212-213. 
  9. [9] E. S. Lander, Symmetric Designs: An Algebraic Approach, Cambridge University Press, Cambridge, 1983. Zbl0502.05010
  10. [10] P. Moree, Psixyology and Diophantine equations, Ph.D. Thesis, Leiden University, 1993. Zbl0784.11046
  11. [11] P. Moree, Counting divisors of Lucas numbers, MPI-Bonn preprint No. 34, 1996. 
  12. [12] R. W. K. Odoni, A conjecture of Krishnamurthy on decimal periods and some allied problems, J. Number Theory 13 (1981), 303-319. Zbl0471.10031
  13. [13] R. W. K. Odoni, A problem of Rankin on sums of powers of cusp-form coefficients, J. London Math. Soc. 44 (1991), 203-217. Zbl0757.11014
  14. [14] V. Pless, P. Solé and Z. Qian, Cyclic self dual ℤ₄-codes, Finite Fields Appl. 3 (1997), 48-69. Zbl1053.94573
  15. [15] A. G. Postnikov, Introduction to Analytic Number Theory, Transl. Math. Monographs 68, Amer. Math. Soc., Providence, R.I., 1988. Zbl0641.10001
  16. [16] A. R. Rajwade, Squares, Cambridge University Press, 1993. 
  17. [17] W. Sierpi/nski, Sur une décomposition des nombres premiers en deux classes, Collect. Math. 10 (1958), 81-83. 
  18. [18] K. Wiertelak, On the density of some sets of primes. I, II, Acta Arith. 34 (1977/78), 183-196, 197-210. Zbl0373.10029
  19. [19] K. Wiertelak, On the density of some sets of primes. III, Funct. Approx. Comment. Math. 10 (1981), 93-103. Zbl0461.10039
  20. [20] K. Wiertelak, On the density of some sets of primes. IV, Acta Arith. 43 (1984), 177-190. Zbl0531.10049
  21. [21] K. Wiertelak, On the density of some sets of primes p, for which o r d p ( n ) = d , Funct. Approx. Comment. Math. 21 (1992), 69-73. Zbl0780.11045

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