Complete solution of a family of simultaneous Pellian equations

 Access to full text

 Full (PDF)

1. Baker A., 10.1112/jlms/s1-43.1.1, J. London Math. Soc 43 (1968), 1-9. (1968) Zbl0157.09801MR0231783DOI10.1112/jlms/s1-43.1.1
2. Baker A., Davenport H., 10.1093/qmath/20.1.129, Quart. J. Math. Oxford Ser. (2) 20 (1969), 129-137. (1969) MR0248079DOI10.1093/qmath/20.1.129
3. Bennett M.A., On the number of solutions of simultaneous Pell equations, J. Reine Angew. Math., to appear. Zbl1165.11034MR1629862
4. Brown E., Sets in which xy + k is always a square, Math. Comp. 45 (1985), 613-620. (1985) Zbl0577.10015MR0804949
5. Cohn J. H. E., Lucas and Fibonacci numbers and some Diophantine equations, Proc. Glasgow Math. Assoc. 7 (1965), 24-28. (1965) Zbl0127.01902MR0177944
6. Dickson L. E., History of the Theory of Numbers, Vol. 2, Chelsea, New York, 1966, pp. 518-519. (1966) 
7. Diophantus of Alexandria, Arithmetics and the Book of Polygonal Numbers, (I.G. Bashmakova, Ed.), Nauka, Moscow, 1974 (in Russian), pp. 103-104, 232. (1974) 
8. Dujella A., Generalization of a problem of Diophantus, Acta Arith. 65 (1993), 15-27. (1993) Zbl0849.11018MR1239240
9. Dujella A., The problem of the extension of a parametric family of Diophantine triples, Publ. Math. Debrecen 51 (1997), 311-322. (1997) Zbl0903.11010MR1485226
10. Dujella A., A proof of the Hoggatt-Bergum conjecture, Proc. Amer. Math. Soc., to appear. Zbl0937.11011MR1605956
11. Dujella A., An extension of an old problem of Diophantus and Euler, (preprint). Zbl1125.11308MR1730070
12. Dujella A., Petho A., Generalization of a theorem of Baker and Davenport, Quart. J. Math. Oxford Ser. (2), to appear. 
13. Gupta H. K., Singh K., 10.1155/S0161171285000886, Internat. J. Math. Math. Sci. 5 (1985), 799-804. (1985) Zbl0585.10006MR0821637DOI10.1155/S0161171285000886
14. Kedlaya K. S., Solving constrained Pell equations, Math. Comp., to appear. Zbl0945.11027MR1443123
15. Mohanty S. P., Ramasamy A. M. S., 10.1016/0022-314X(84)90068-4, J. Number Theory 18 (1984), 356-359. (1984) MR0746870DOI10.1016/0022-314X(84)90068-4
16. Mohanty S. P., Ramasamy A.M.S., On $P_{r,k}$ sequences, Fibonacci Quart. 23 (1985), 36-44. (1985) MR0786359
17. Nagell T., Introduction to Number Theory, Almqvist, Stockholm, Wiley, New York, 1951. (1951) Zbl0042.26702MR0043111
18. Rickert J. H., 10.1017/S0305004100076118, Math. Proc. Cambridge Philos. Soc. 113 (1993), 461-472. (1993) Zbl0786.11040MR1207511DOI10.1017/S0305004100076118
19. SIMATH Manual, Universität des Saarlandes, Saarbrücken, 1993. (1993)