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Volumn 125, Issue 2, 2007, Pages 356-392

On the number of solutions to systems of Pell equations

Author keywords

Linear forms in logarithms; Simultaneous Pell equations

Indexed keywords


EID: 34249037152     PISSN: 0022314X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnt.2006.09.016     Document Type: Article
Times cited : (22)

References (32)
  • 2
    • 0030353140 scopus 로고    scopus 로고
    • Simultaneous Pell equations
    • Anglin W.S. Simultaneous Pell equations. Math. Comp. 65 (1996) 355-359
    • (1996) Math. Comp. , vol.65 , pp. 355-359
    • Anglin, W.S.1
  • 3
    • 84974028756 scopus 로고
    • Linear forms in the logarithms of algebraic numbers, IV
    • Baker A. Linear forms in the logarithms of algebraic numbers, IV. Mathematika 15 (1968) 204-216
    • (1968) Mathematika , vol.15 , pp. 204-216
    • Baker, A.1
  • 6
    • 0041022312 scopus 로고    scopus 로고
    • On the number of solutions of simultaneous Pell equations
    • Bennett M.A. On the number of solutions of simultaneous Pell equations. J. Reine Angew. Math. 498 (1998) 173-199
    • (1998) J. Reine Angew. Math. , vol.498 , pp. 173-199
    • Bennett, M.A.1
  • 7
    • 33745643374 scopus 로고    scopus 로고
    • On the number of solutions of simultaneous Pell equations, II
    • Bennett M.A., Cipu M., Mignotte M., and Okazaki R. On the number of solutions of simultaneous Pell equations, II. Acta Arith. 122 (2006) 407-417
    • (2006) Acta Arith. , vol.122 , pp. 407-417
    • Bennett, M.A.1    Cipu, M.2    Mignotte, M.3    Okazaki, R.4
  • 8
    • 84966212584 scopus 로고
    • Sets in which x y + k is always a square
    • Brown E. Sets in which x y + k is always a square. Math. Comp. 45 172 (1985) 613-620
    • (1985) Math. Comp. , vol.45 , Issue.172 , pp. 613-620
    • Brown, E.1
  • 9
    • 34248997088 scopus 로고    scopus 로고
    • M. Cipu, Pairs of Pell equations having at most one common solution in positive integers, submitted for publication
  • 11
    • 0009892692 scopus 로고    scopus 로고
    • Complete solution of a family of simultaneous Pellian equations
    • Dujella A. Complete solution of a family of simultaneous Pellian equations. Acta Math. Inform. Univ. Ostraviensis 6 (1998) 59-67
    • (1998) Acta Math. Inform. Univ. Ostraviensis , vol.6 , pp. 59-67
    • Dujella, A.1
  • 12
    • 0032221914 scopus 로고    scopus 로고
    • A generalization of a theorem of Baker and Davenport
    • Dujella A., and Petho{combining double acute accent} A. A generalization of a theorem of Baker and Davenport. Quart. J. Math. Oxford Ser. (2) 49 (1998) 291-306
    • (1998) Quart. J. Math. Oxford Ser. (2) , vol.49 , pp. 291-306
    • Dujella, A.1    Petho, A.2
  • 13
    • 0000285988 scopus 로고
    • On a method of solving a class of Diophantine equations
    • Grinstead C.M. On a method of solving a class of Diophantine equations. Math. Comp. 32 143 (1978) 936-940
    • (1978) Math. Comp. , vol.32 , Issue.143 , pp. 936-940
    • Grinstead, C.M.1
  • 14
    • 58149363345 scopus 로고
    • Formes linéaires en deux logarithmes et déterminants d'interpolation
    • Laurent M., Mignotte M., and Nesterenko Yu. Formes linéaires en deux logarithmes et déterminants d'interpolation. J. Number Theory 55 (1995) 285-321
    • (1995) J. Number Theory , vol.55 , pp. 285-321
    • Laurent, M.1    Mignotte, M.2    Nesterenko, Yu.3
  • 16
    • 0346854520 scopus 로고    scopus 로고
    • An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers, II
    • (in Russian). English translation in:
    • Matveev E.M. An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers, II. Izv. Ross. Akad. Nauk Ser. Mat. 64 (2000) 125-180 (in Russian). English translation in:
    • (2000) Izv. Ross. Akad. Nauk Ser. Mat. , vol.64 , pp. 125-180
    • Matveev, E.M.1
  • 17
    • 0346854520 scopus 로고    scopus 로고
    • An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers, II
    • Matveev E.M. An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers, II. Izv. Math. 64 (2000) 1217-1269
    • (2000) Izv. Math. , vol.64 , pp. 1217-1269
    • Matveev, E.M.1
  • 18
    • 0003268606 scopus 로고
    • The g.c.d. in Lucas sequences and Lehmer number sequences
    • McDaniel W.L. The g.c.d. in Lucas sequences and Lehmer number sequences. Fibonacci Quart. 29 (1991) 24-29
    • (1991) Fibonacci Quart. , vol.29 , pp. 24-29
    • McDaniel, W.L.1
  • 19
    • 0012293332 scopus 로고    scopus 로고
    • A corollary to a theorem of Laurent-Mignotte-Nesterenko
    • Mignotte M. A corollary to a theorem of Laurent-Mignotte-Nesterenko. Acta Arith. 86 (1998) 101-111
    • (1998) Acta Arith. , vol.86 , pp. 101-111
    • Mignotte, M.1
  • 21
    • 0030459295 scopus 로고    scopus 로고
    • Euler's concordant forms
    • Ono K. Euler's concordant forms. Acta Arith. 78 (1996) 101-123
    • (1996) Acta Arith. , vol.78 , pp. 101-123
    • Ono, K.1
  • 23
    • 0011357631 scopus 로고
    • The number of subspaces occurring in the p-adic subspace theorem in Diophantine approximation
    • Schlickewei H.P. The number of subspaces occurring in the p-adic subspace theorem in Diophantine approximation. J. Reine Angew. Math. 406 (1990) 44-108
    • (1990) J. Reine Angew. Math. , vol.406 , pp. 44-108
    • Schlickewei, H.P.1
  • 24
    • 0001099678 scopus 로고
    • Norm form equations
    • Schmidt W.M. Norm form equations. Ann. of Math. 96 (1972) 526-551
    • (1972) Ann. of Math. , vol.96 , pp. 526-551
    • Schmidt, W.M.1
  • 25
    • 0003304303 scopus 로고
    • Diophantine Approximation
    • Springer
    • Schmidt W.M. Diophantine Approximation. Lecture Notes in Math. vol. 785 (1980), Springer
    • (1980) Lecture Notes in Math. , vol.785
    • Schmidt, W.M.1
  • 26
    • 0001764679 scopus 로고
    • Über einige Anwendungen diophantischer Approximationen
    • Siegel C.L. Über einige Anwendungen diophantischer Approximationen. Abh. Preuss. Akad. Wiss. 1 (1929) 1-70
    • (1929) Abh. Preuss. Akad. Wiss. , vol.1 , pp. 1-70
    • Siegel, C.L.1
  • 27
    • 84941462766 scopus 로고
    • Über Annäherungswerte algebraischer Zahlen
    • Thue A. Über Annäherungswerte algebraischer Zahlen. J. Reine Angew. Math. 135 (1909) 284-305
    • (1909) J. Reine Angew. Math. , vol.135 , pp. 284-305
    • Thue, A.1
  • 28
    • 0041330432 scopus 로고    scopus 로고
    • Effective solution of two simultaneous Pell equations by the elliptic logarithm method
    • Tzanakis N. Effective solution of two simultaneous Pell equations by the elliptic logarithm method. Acta Arith. 103 (2002) 119-135
    • (2002) Acta Arith. , vol.103 , pp. 119-135
    • Tzanakis, N.1
  • 29
    • 0033479689 scopus 로고    scopus 로고
    • On two classes of simultaneous Pell equations with no solutions
    • Walsh P.G. On two classes of simultaneous Pell equations with no solutions. Math. Comp. 68 225 (1999) 385-388
    • (1999) Math. Comp. , vol.68 , Issue.225 , pp. 385-388
    • Walsh, P.G.1
  • 30
    • 0041330495 scopus 로고    scopus 로고
    • On the number of solutions of simultaneous Pell equations
    • Yuan P. On the number of solutions of simultaneous Pell equations. Acta Arith. 101 (2002) 215-221
    • (2002) Acta Arith. , vol.101 , pp. 215-221
    • Yuan, P.1
  • 31
    • 18444413529 scopus 로고    scopus 로고
    • Simultaneous Pell equations
    • Yuan P. Simultaneous Pell equations. Acta Arith. 115 (2004) 119-131
    • (2004) Acta Arith. , vol.115 , pp. 119-131
    • Yuan, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.