The Diophantine equation x 2 + q m = p n

Nobuhiro Terai

Acta Arithmetica (1993)

  • Volume: 63, Issue: 4, page 351-358
  • ISSN: 0065-1036

How to cite

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Nobuhiro Terai. "The Diophantine equation $x^2 + q^m =p^n$." Acta Arithmetica 63.4 (1993): 351-358. <http://eudml.org/doc/206526>.

@article{NobuhiroTerai1993,
author = {Nobuhiro Terai},
journal = {Acta Arithmetica},
keywords = {exponential diophantine equation; ideal class group; positive integral solution},
language = {eng},
number = {4},
pages = {351-358},
title = {The Diophantine equation $x^2 + q^m =p^n$},
url = {http://eudml.org/doc/206526},
volume = {63},
year = {1993},
}

TY - JOUR
AU - Nobuhiro Terai
TI - The Diophantine equation $x^2 + q^m =p^n$
JO - Acta Arithmetica
PY - 1993
VL - 63
IS - 4
SP - 351
EP - 358
LA - eng
KW - exponential diophantine equation; ideal class group; positive integral solution
UR - http://eudml.org/doc/206526
ER -

References

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  1. [1] R. Alter and K. K. Kubota, The diophantine equation x² + D =pⁿ, Pacific J. Math. (1) 46 (1973), 11-16. Zbl0224.10016
  2. [2] L. Jeśmanowicz, Kilka uwag o liczbach pitagorejskich [ Some remarks on Pythagorean numbers], Wiadom. Mat. 1 (1956), 196-202. Zbl0074.27205
  3. [3] W. Ljunggren, Zur Theorie der Gleichung x² + 1=Dy⁴, Avh. Norske Vid. Akad. Oslo 5 (1942), 1-27. Zbl0027.01103
  4. [4] W. Sierpiński, O równaniu 3 x + 4 y = 5 z [On the equation 3 x + 4 y = 5 z ], Wiadom. Mat. 1 (1956), 194-195. 
  5. [5] W. Sierpiński, Elementary Theory of Numbers, PWN-Polish Scientific Publishers, Warszawa 1988. Zbl0638.10001
  6. [6] C. Störmer, L'équation m arctan(1/x) +n arctan(1/y) = k(π/4), Bull. Soc. Math. France 27 (1899), 160-170. 

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