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International Journal of Mathematics and Mathematical Sciences
Volume 2005, Issue 14, Pages 2217-2226
http://dx.doi.org/10.1155/IJMMS.2005.2217

Nonextendibility of D(1)-triples of the form {1,10,c}

Department of Mathematics, Faculty of Civil Engineering, University of Zagreb, Fra Andrije Kačića-Miošića 26, Zagreb 10000, Croatia

Received 4 March 2005; Revised 21 June 2005

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [13 citations]

The following is the list of published articles that have cited the current article.

  • Yasutsugu Fujita, “The non-extensibility of D(4k)-triples {1, 4k(k - 1), 4k2 + 1} with k prime,” Glasnik Matematicki, vol. 41, no. 2, pp. 205–216, 2006. View at Publisher · View at Google Scholar
  • Andrej Dujella, Alan Filipin, and Clemens Fuchs, “Effective solution of the D(-1)-quadruple conjecture,” Acta Arithmetica, vol. 128, no. 4, pp. 319–338, 2007. View at Publisher · View at Google Scholar
  • Yasutsugu Fujita, “The D(1)-extensions of D(-1)-triples {1, 2, c} and integer points on the attached elliptic curves,” Acta Arithmetica, vol. 128, no. 4, pp. 349–375, 2007. View at Publisher · View at Google Scholar
  • Yasutsugu Fujita, “Extensions of the D(∓k 2)-triples {k 2, k 2 ± 1, 4k 2 ± 1},” Periodica Mathematica Hungarica, vol. 59, no. 1, pp. 81–98, 2009. View at Publisher · View at Google Scholar
  • Bo He, and Alain Togbé, “On the family of diophantine triples {k + 1, 4k, 9k + 3},” Periodica Mathematica Hungarica, vol. 58, no. 1, pp. 59–70, 2009. View at Publisher · View at Google Scholar
  • B. He, and A. Togbé, “On a family of diophantine triples {k, A 2 k + 2A, (A + 1)2 k + 2 (A + 1)} with two parameters,” Acta Mathematica Hungarica, vol. 124, no. 1-2, pp. 99–113, 2009. View at Publisher · View at Google Scholar
  • Yasutsugu Fujita, “The hoggatt-bergum conjecture on D(-1)-triples {F2k+1, F 2k+3, F2k+5} and integer points on the attached elliptic curves,” Rocky Mountain Journal of Mathematics, vol. 39, no. 6, pp. 1907–1932, 2009. View at Publisher · View at Google Scholar
  • Bo He, and Alain Togbé, “On the -triple and its unique -extension,” Journal of Number Theory, vol. 131, no. 1, pp. 120–137, 2011. View at Publisher · View at Google Scholar
  • Alan Filipin, Yasutsugu Fujita, and Maurice Mignotte, “The Non-Extendibility Of Some Parametric Families Of D(-1)-Triples,” Quarterly Journal Of Mathematics, vol. 63, no. 3, pp. 605–621, 2012. View at Publisher · View at Google Scholar
  • Nicolae Ciprian Bonciocat, Mutat Cipu, and Maurice Mignotte, “On D(-1)-Quadruples,” Publicacions Matematiques, vol. 56, no. 2, pp. 279–304, 2012. View at Publisher · View at Google Scholar
  • Nicolae Ciprian Bonciocat, Mihai Cipu, and Maurice Mignotte, “On D(-1)-quadruples,” Publicacions Matematiques, vol. 56, no. 2, pp. 279–304, 2012. View at Publisher · View at Google Scholar
  • Ivan Soldo, “On the extensibility of D(−1)-triples {1, b, c} in the ring $$\mathbb{Z}\left[ {\sqrt { - t} } \right]$$, t > 0,” Studia Scientiarum Mathematicarum Hungarica, vol. 50, no. 3, pp. 296–330, 2013. View at Publisher · View at Google Scholar
  • Ivan Soldo, “$$D(-1)$$ D ( - 1 ) -triples of the Form $$\{1,b,c\}$$ { 1 , b , c } in the Ring $${\mathbb {Z}}[\sqrt{-t}], t>0$$ Z [ - t ] , t > 0,” Bulletin of the Malaysian Mathematical Sciences Society, 2015. View at Publisher · View at Google Scholar