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1993 | 65 | 4 | 367-381
Tytuł artykułu

The diophantine equation x² + C = yⁿ

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
65
Numer
4
Strony
367-381
Opis fizyczny
Daty
wydano
1993
otrzymano
1992-11-27
poprawiono
1993-06-25
Twórcy
  • Department of Mathematics, Royal Holloway and Bedford New College, Egham, Surrey TW20 OEX, England
Bibliografia
  • [1] A. Aigner, Die diophantische Gleichung $x²+4D=y^p$ im Zusammenhang mit Klassenzahlen, Monatsh. Math. 72 (1968), 1-5.
  • [2] J. Blass, A note on diophantine equation Y²+k=X⁵, Math. Comp. 30 (1976), 638-640.
  • [3] J. Blass and R. Steiner, On the equation y²+k=x⁷, Utilitas Math. 13 (1978), 293-297.
  • [4] E. Brown, Diophantine equations of the form x²+D=yⁿ, J. Reine Angew. Math. 274/275 (1975), 385-389.
  • [5] E. Brown, Diophantine equations of the form $ax²+Db²=y^p$, J. Reine Angew. Math. 291 (1977), 118-127.
  • [6] K. Chao, On the diophantine equation x²=yⁿ+1, xy≠0, Sci. Sinica (Notes) 14 (1964), 457-460.
  • [7] F. B. Coghlan and N. M. Stephens, The diophantine equation x³-y²=k, in: Computers in Number Theory, Academic Press, London, 1971, 199-205.
  • [8] E. L. Cohen, Sur l'équation diophantienne $x²+11=3^k$, C. R. Acad. Sci. Paris Sér. A 275 (1972), 5-7.
  • [9] E. L. Cohen, On the Ramanujan-Nagell equation and its generalizations, in: Proc. First Conference of the Canadian Number Theory Association, Banff, Alberta, 1988, de Gruyter, 1990, 81-92.
  • [10] J. H. E. Cohn, The Diophantine equation x²+3=yⁿ, Glasgow Math. J. 35 (1993), 203-206.
  • [11] J. H. E. Cohn, The diophantine equation x²+19=yⁿ, Acta Arith. 61 (1992), 193-197.
  • [12] J. H. E. Cohn, The diophantine equation x²+2^k=yⁿ, Arch. Math. (Basel) 59 (1992), 341-344.
  • [13] J. H. E. Cohn, Lucas and Fibonacci numbers and some Diophantine equations, Proc. Glasgow Math. Assoc. 7 (1965), 24-28.
  • [14] L. Euler, Algebra, Vol. 2.
  • [15] O. Korhonen, On the Diophantine equation Ax²+8B=yⁿ, Acta Univ. Oulu. Ser. A Sci. Rerum Natur. Math. 16 (1979).
  • [16] O. Korhonen, On the Diophantine equation Ax²+2B=yⁿ, Acta Univ. Oulu. Ser. A Sci. Rerum Natur. Math. 17 (1979).
  • [17] O. Korhonen, On the Diophantine equation Cx²+D=yⁿ, Acta Univ. Oulu. Ser. A Sci. Rerum Natur. Math. 25 (1981).
  • [18] V. A. Lebesgue, Sur l'impossibilité en nombres entiers de l'équation $x^m=y²+1$, Nouvelles Annales des Mathématiques (1) 9 (1850), 178-181.
  • [19] W. Ljunggren, On the diophantine equation x²+p²=yⁿ, Norske Vid. Selsk. Forh. Trondheim 16 (8) (1943), 27-30.
  • [20] W. Ljunggren, Über einige Arcustangensgleichungen die auf interessante unbestimmte Gleichungen führen, Ark. Mat. Astr. Fys. 29A (1943), no. 13.
  • [21] W. Ljunggren, On the diophantine equation x²+D=yⁿ, Norske Vid. Selsk. Forh. Trondheim 17 (23) (1944), 93-96.
  • [22] W. Ljunggren, On a diophantine equation, Norske Vid. Selsk. Forh. Trondheim 18 (32) (1945), 125-128.
  • [23] W. Ljunggren, New theorems concerning the diophantine equation Cx²+D=yⁿ, Norske Vid. Selsk. Forh. Trondheim 29 (1) (1956), 1-4.
  • [24] W. Ljunggren, On the diophantine equation y²-k=x³, Acta Arith. 8 (1963), 451-463.
  • [25] W. Ljunggren, On the diophantine equation Cx²+D=yⁿ, Pacific J. Math. 14 (1964), 585-596.
  • [26] W. Ljunggren, On the diophantine equation Cx²+D=2yⁿ, Math. Scand. 18 (1966), 69-86.
  • [27] W. Ljunggren, New theorems concerning the diophantine equation $x²+D=4y^q$, Acta Arith. 21 (1972), 183-191.
  • [28] L. J. Mordell, Diophantine Equations, Academic Press, London, 1969.
  • [29] T. Nagell, Sur l'impossibilité de quelques équations à deux indéterminées, Norsk. Mat. Forensings Skrifter No. 13 (1923), 65-82.
  • [30] T. Nagell, Løsning til oppgave nr 2, 1943, s. 29, Norske Mat. Tidsskrift 30 (1948), 62-64.
  • [31] T. Nagell, Verallgemeinerung eines Fermatschen Satzes, Arch. Math. (Basel) 5 (1954), 153-159.
  • [32] T. Nagell, Contributions to the theory of a category of diophantine equations of the second degree with two unknowns, Nova Acta Regiae Soc. Sci. Upsaliensis (4) 16 (2) (1955).
  • [33] T. Nagell, On the Diophantine equation x²+8D=yⁿ, Ark. Mat. 3 (1954), 103-112.
  • [34] S. Ramanujan, Question 464, J. Indian Math. Soc. 5 (1913), 120.
  • [35] T. N. Shorey, A. J. van der Poorten, R. Tijdeman and A. Schinzel, Applications of the Gel'fond-Baker method to diophantine equations, in: Transcendence Theory: Advances and Applications, Academic Press, London, 1977, 59-77.
  • [36] T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge University Press, Cambridge, 1986.
  • [37] B. M. E. Wren, y²+D=x⁵, Eureka 36 (1973), 37-38
Typ dokumentu
Bibliografia
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