Have a personal or library account? Click to login
Is there a polynomial D(2X + 1)-quadruple? Cover

References

  1. N. C. Bonciocat, M. Cipu and M. Mignotte, There is no Diophantine D(−1)-quadruple, J. London Math. Soc. 105 (2022), 63–99.
  2. K. Chakraborty, S. Gupta and A. Hoque, On a conjecture of Franušić and Jadrijević: Counter-examples, Results Math. 78 (2023), Article 18.
  3. Diophantus of Alexandria, Arithmetics and the Book of Polygonal Numbers, (I. G. Bashmakova, Ed.) (Nauka 1974), 85–86, 215–217.
  4. A. Dujella, Diophantine m-tuples, https://web.math.pmf.unizg.hr/~duje/dtuples.html
  5. A. Dujella, Generalization of a problem of Diophantus, Acta Arith. 65 (1993), 15–27.
  6. A. Dujella, Some polynomial formulas for Diophantine quadruples, Grazer Math. Ber. 328 (1996), 25–30.
  7. A. Dujella, The problem of Diophantus and Davenport for Gaussian integers, Glas. Mat. Ser. III 32 (1997), 1–10.
  8. A. Dujella and C. Fuchs, Complete solution of the polynomial version of a problem of Diophantus, J. Number Theory 106 (2004), 326–344.
  9. A. Dujella, C. Fuchs and R. F. Tichy, Diophantine m-tuples for linear polynomials, Period. Math. Hungar. 45 (2002), 21–33.
  10. A. Dujella, C. Fuchs and G. Walsh, Diophantine m-tuples for linear polynomials. II. Equal degrees, J. Number Theory, 120 (2006), 213–228.
  11. A. Dujella and A. Jurasić, On the size of sets in a polynomial variant of a problem of Diophantus, Int. J. Number Theory, 6 (2010), 1449–1471.
  12. A. Dujella and A. Jurasić, Some Diophantine triples and quadruples for quadratic polynomials, J. Comb. Number Theory 3(2) (2011), 123141.
  13. A. Dujella and F. Luca, On a problem of Diophantus with polynomials, Rocky Mountain J. Math., 37 (2007), 131–157.
  14. A. Filipin and A. Jurasić, A polynomial variant of a problem of Diophantus and its consequences, Glas. Mat. Ser. III, 54 (2019), 21–52.
  15. A. Filipin and A. Jurasić, On the size of Diophantine m-tuples for linear polynomials, Miskolc Math. Notes, 17 (2016), 2; 861–876.
  16. [16] Z. Franušić, A Diophantine problem in [ (1+d)/2 ] \mathbb{Z}\left[ {\left( {1 + \sqrt d } \right)/2} \right] , Studia Sci. Math. Hungar. 46 (2009), 103–112.
  17. [17] Z. Franušić, Diophantine quadruples in the ring of integers of (23) \mathbb{Q}\left( {\root 3 \of 2 } \right) , Miskolc Math. Notes 14 (2013), 893–903.
  18. [18] Z. Franušić, Diophantine quadruples in the ring [ 2 ] \mathbb{Z}\left[ {\sqrt 2 } \right] , Math. Commun. 9 (2004), 141–148.
  19. [19] Z. Franušić, Diophantine quadruples in [ 4k+3 ] \mathbb{Z}\left[ {\sqrt {4k + 3} } \right] , Ramanujan J. 17 (2008), 77–88.
  20. [20] Z. Franušić and B. Jadrijević, D(n)-quadruples in the ring of integers of (2,3) \mathbb{Q}\left( {\sqrt 2 ,\sqrt 3 } \right) , Math. Slovaca 69 (2019), 1263–1278.
  21. Z. Franušić and A. Jurasić, On nonexistence of D(n)-quadruples, Math. Slovaca 74 (2024), No. 4, 835–844
  22. [22] Z. Franušić and I. Soldo, The problem of Diophantus for integers of (-3) \mathbb{Q}\left( {\sqrt { - 3} } \right) , Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 18 (2014), 15–25.
  23. B. W. Jones, A second variation of a problem of Davenport and Diophantus, Fibonacci Quart. 15 (1977), 323–330.
  24. B. W. Jones, A variation of a problem of Davenport and Diophantus, Quart. J. Math. Oxford Ser. (2) 27 (1976), 349–353.
  25. LJ. Jukić Matić, On D(w)-quadruples in the rings of integers of certain pure number fields, Glas. Mat. Ser. III 49 (2014), 37–46.
DOI: https://doi.org/10.2478/auom-2025-0019 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 67 - 88
Submitted on: Oct 30, 2024
|
Accepted on: Mar 15, 2025
|
Published on: Jun 3, 2025
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2025 Zrinka Franušić, Ana Jurasić, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.