On nonexistence of D(n)-quadruples

References

[1] Bonciocat, N. C.—Cipu, M.—Mignotte, M.: There is no Diophantine D(–1)-quadruple, J. London Math. Soc. 105 (2022), 63–99.10.1112/jlms.12507Search in Google Scholar

[2] Brown, E.: Sets in which xy + k is always a square, Math. Comp. 45 (1985), 613–620.10.1090/S0025-5718-1985-0804949-7Search in Google Scholar

[3] Chakraborty, K.—Gupta, S.—Hoque, A.: On a conjecture of Franušić and Jadrijević: Counter-examples, Results Math. 78 (2023), Art. 18.10.1007/s00025-022-01794-2Search in Google Scholar

[4] Dujella, A.: Diophantine m-tuples, https://web.math.pmf.unizg.hr/duje/dtuples.html.Search in Google Scholar

[5] Dujella, A.: Generalization of a problem of Diophantus, Acta Arith. 65 (1993), 15–27.10.4064/aa-65-1-15-27Search in Google Scholar

[6] Dujella, A.: Number Theory, Školska knjiga, Zagreb, 2021.Search in Google Scholar

[7] Dujella, A.: Some polynomial formulas for Diophantine quadruples, Grazer Math. Ber. 328 (1996), 25–30.Search in Google Scholar

[8] Dujella, A.: The problem of Diophantus and Davenport for Gaussian integers, Glas. Mat. Ser. III 32 (1997), 1–10.Search in Google Scholar

[9] Dujella, A.: On the exceptional set in the problem of Diophantus and Davenport. Application of Fibonacci Numbers (G. E. Bergum, A. N. Philippou, A. F. Horadam, eds.), Vol. 7, Kluwer, Dordrecht, 1998, pp. 69–76.10.1007/978-94-011-5020-0_10Search in Google Scholar

[10] Dujella, A.: What is … a Diophantine m-tuple?, Notices Amer. Math. Soc. 63 (2016), 772–774.10.1090/noti1404Search in Google Scholar

[11] Dujella, A. —Fuchs, C.: A polynomial variant of a problem of Diophantus and Euler, Rocky Mountain J. Math. 33 (2003), 797–811.10.1216/rmjm/1181069929Search in Google Scholar

[12] Dujella, A.—Fuchs, C.—Walsh, G.: Diophantine m-tuples for linear polynomials. II. Equal degrees, J. Number Theory 120 (2006), 213–228.10.1016/j.jnt.2005.12.005Search in Google Scholar

[13] Dujella, A.—Jurasić, A.: Some Diophantine triples and quadruples for quadratic polynomials, J. Comb. Number Theory 3(2) (2011), 123–141.Search in Google Scholar

[14] Dujella, A.—Soldo, I.: Diophantine quadruples in Z[−2] , An. Stiint. Univ. “Ovidius” Constanta Ser. Mat. 18 (2010), 81–98.Search in Google Scholar

[15] Franušić, Z.: Diophantine quadruples in the ring Z[2] , Math. Commun. 9 (2004), 141–148.Search in Google Scholar

[16] Franušić, Z.: A Diophantine problem in Z[(1+d)/2] , Studia Sci. Math. Hungar. 46 (2009), 103–112.10.1556/sscmath.2008.1076Search in Google Scholar

[17] Franušić, Z.: Diophantine quadruples in Z[4k+3] , Ramanujan J. 17 (2008), 77–88.10.1007/s11139-007-9015-ySearch in Google Scholar

[18] Franušić, Z.: Diophantine quadruples in the ring of integers of Q(23) , Miskolc Math. Notes 14 (2013), 893–903.10.18514/MMN.2013.753Search in Google Scholar

[19] Franušić, Z.—Jadrijević, B.: D(n)-quadruples in the ring of integers of Q(2,3) , Math. Slovaca 69 (2019), 1263–1278.10.1515/ms-2017-0307Search in Google Scholar

[20] Franušić, Z.—Soldo, I.: The problem of Diophantus for integers of Q(−3) , Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 18 (2014), 15–25.Search in Google Scholar

[21] Gibbs, P.: Adjugates of Diophantine Quadruples, Integers 10 (2010), 201–209.10.1515/integ.2010.015Search in Google Scholar

[22] Gupta, H.—Singh, K.: On k-triad sequences, Internat. J. Math. Math. Sci. 5 (1985), 799–804.10.1155/S0161171285000886Search in Google Scholar

[23] Jukić Matić, LJ.: On D(w)-quadruples in the rings of integers of certain pure number fields, Glas. Mat. Ser. III 49 (2014), 37–46.10.3336/gm.49.1.04Search in Google Scholar

[24] Jurasić, A.: Diophantine m-tuples for quadratic polynomials, Glas. Mat. Ser. III 46 (2011), 283–309.10.3336/gm.46.2.02Search in Google Scholar

[25] Mohanty, S. P.—Ramasamy, A. M. S.: On P_r,k sequences, Fibonacci Quart. 23 (1985), 36–44.10.1080/00150517.1985.12429852Search in Google Scholar