On the diophantine equation x y + y z + z x = d

Stéphane Louboutin; M. F. Newman

Acta Mathematica et Informatica Universitatis Ostraviensis (1998)

  • Volume: 06, Issue: 1, page 155-158
  • ISSN: 1804-1388

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Louboutin, Stéphane, and Newman, M. F.. "On the diophantine equation $xy+yz+zx=d$." Acta Mathematica et Informatica Universitatis Ostraviensis 06.1 (1998): 155-158. <http://eudml.org/doc/23807>.

@article{Louboutin1998,
author = {Louboutin, Stéphane, Newman, M. F.},
journal = {Acta Mathematica et Informatica Universitatis Ostraviensis},
keywords = {ternary quadratic forms; quadratic Diophantine equations; ideal class groups; imaginary quadratic fields},
language = {eng},
number = {1},
pages = {155-158},
publisher = {University of Ostrava},
title = {On the diophantine equation $xy+yz+zx=d$},
url = {http://eudml.org/doc/23807},
volume = {06},
year = {1998},
}

TY - JOUR
AU - Louboutin, Stéphane
AU - Newman, M. F.
TI - On the diophantine equation $xy+yz+zx=d$
JO - Acta Mathematica et Informatica Universitatis Ostraviensis
PY - 1998
PB - University of Ostrava
VL - 06
IS - 1
SP - 155
EP - 158
LA - eng
KW - ternary quadratic forms; quadratic Diophantine equations; ideal class groups; imaginary quadratic fields
UR - http://eudml.org/doc/23807
ER -

References

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  1. T. Cai, On the diophantine equation x y + y z + z x = m , Publ. Math. Debrecen 45 (1994), 131-132. (1994) Zbl0864.11015MR1291808
  2. D. Cox, Primes of the form x 2 + n y 2 , John Wiley & Sons (1989). (1989) MR1028322
  3. N. A. Hall, 10.1007/BF01210641, Math. Zeit. 44 (1938), 85-90. (1938) DOI10.1007/BF01210641
  4. Al-Zaid Hassan B. Brindza, Á. Pintér, 10.4153/CMB-1996-024-5, Canad. Math. Bull. 39 (1996), 199-202. (1996) MR1390355DOI10.4153/CMB-1996-024-5
  5. K. Kovács, About some positive solutions of the diophantine equation ∑ 1 ≤ i < j ≤ n a i a j = m , Publ Math. Debrecen 40 (1992), 207-210. (1992) MR1181363
  6. S. Louboutin, Minorations (sous ľhypothèse de Riemann généralisée) des nombres de classes des corps quadratiques imaginaires, Application, C. R. Acad. Sci. Paris 310 (1990), 795-800. (1990) MR1058499
  7. L. J. Mordell, Diophantine equations, Chapter 30, Section 2 : The equation xy + yz + zx = d, Academic Press (1969). (1969) Zbl0188.34503MR0249355
  8. T. Tatuzawa, On a theorem of Siegel, Japan J. Math. 21 (1951), 163-178. (1951) Zbl0054.02302MR0051262

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