The diophantine equation x² + C = yⁿ
J. H. E. Cohn
Acta Arithmetica, Tome 64 (1993), p. 367-381 / Harvested from The Polish Digital Mathematics Library
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     author = {J. H. E. Cohn},
     title = {The diophantine equation x2 + C = yn},
     journal = {Acta Arithmetica},
     volume = {64},
     year = {1993},
     pages = {367-381},
     zbl = {0795.11016},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav65i4p367bwm}
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J. H. E. Cohn. The diophantine equation x² + C = yⁿ. Acta Arithmetica, Tome 64 (1993) pp. 367-381. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav65i4p367bwm/

[000] [1] A. Aigner, Die diophantische Gleichung x²+4D=yp im Zusammenhang mit Klassenzahlen, Monatsh. Math. 72 (1968), 1-5. | Zbl 0164.04805

[001] [2] J. Blass, A note on diophantine equation Y²+k=X⁵, Math. Comp. 30 (1976), 638-640. | Zbl 0336.10012

[002] [3] J. Blass and R. Steiner, On the equation y²+k=x⁷, Utilitas Math. 13 (1978), 293-297. | Zbl 0375.10010

[003] [4] E. Brown, Diophantine equations of the form x²+D=yⁿ, J. Reine Angew. Math. 274/275 (1975), 385-389. | Zbl 0303.10014

[004] [5] E. Brown, Diophantine equations of the form ax²+Db²=yp, J. Reine Angew. Math. 291 (1977), 118-127. | Zbl 0338.10018

[005] [6] K. Chao, On the diophantine equation x²=yⁿ+1, xy≠0, Sci. Sinica (Notes) 14 (1964), 457-460.

[006] [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.

[007] [8] E. L. Cohen, Sur l’équation diophantienne x²+11=3k, C. R. Acad. Sci. Paris Sér. A 275 (1972), 5-7. | Zbl 0236.10008

[008] [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.

[009] [10] J. H. E. Cohn, The Diophantine equation x²+3=yⁿ, Glasgow Math. J. 35 (1993), 203-206.

[010] [11] J. H. E. Cohn, The diophantine equation x²+19=yⁿ, Acta Arith. 61 (1992), 193-197. | Zbl 0770.11018

[011] [12] J. H. E. Cohn, The diophantine equation x²+2^k=yⁿ, Arch. Math. (Basel) 59 (1992), 341-344. | Zbl 0770.11019

[012] [13] J. H. E. Cohn, Lucas and Fibonacci numbers and some Diophantine equations, Proc. Glasgow Math. Assoc. 7 (1965), 24-28. | Zbl 0127.01902

[013] [14] L. Euler, Algebra, Vol. 2.

[014] [15] O. Korhonen, On the Diophantine equation Ax²+8B=yⁿ, Acta Univ. Oulu. Ser. A Sci. Rerum Natur. Math. 16 (1979). | Zbl 0414.10007

[015] [16] O. Korhonen, On the Diophantine equation Ax²+2B=yⁿ, Acta Univ. Oulu. Ser. A Sci. Rerum Natur. Math. 17 (1979). | Zbl 0416.10012

[016] [17] O. Korhonen, On the Diophantine equation Cx²+D=yⁿ, Acta Univ. Oulu. Ser. A Sci. Rerum Natur. Math. 25 (1981). | Zbl 0452.10018

[017] [18] V. A. Lebesgue, Sur l’impossibilité en nombres entiers de l’équation xm=y²+1, Nouvelles Annales des Mathématiques (1) 9 (1850), 178-181.

[018] [19] W. Ljunggren, On the diophantine equation x²+p²=yⁿ, Norske Vid. Selsk. Forh. Trondheim 16 (8) (1943), 27-30. | Zbl 0060.09106

[019] [20] W. Ljunggren, Über einige Arcustangensgleichungen die auf interessante unbestimmte Gleichungen führen, Ark. Mat. Astr. Fys. 29A (1943), no. 13. | Zbl 0028.10904

[020] [21] W. Ljunggren, On the diophantine equation x²+D=yⁿ, Norske Vid. Selsk. Forh. Trondheim 17 (23) (1944), 93-96. | Zbl 0060.09107

[021] [22] W. Ljunggren, On a diophantine equation, Norske Vid. Selsk. Forh. Trondheim 18 (32) (1945), 125-128. | Zbl 0060.09108

[022] [23] W. Ljunggren, New theorems concerning the diophantine equation Cx²+D=yⁿ, Norske Vid. Selsk. Forh. Trondheim 29 (1) (1956), 1-4.

[023] [24] W. Ljunggren, On the diophantine equation y²-k=x³, Acta Arith. 8 (1963), 451-463. | Zbl 0132.28404

[024] [25] W. Ljunggren, On the diophantine equation Cx²+D=yⁿ, Pacific J. Math. 14 (1964), 585-596. | Zbl 0131.28401

[025] [26] W. Ljunggren, On the diophantine equation Cx²+D=2yⁿ, Math. Scand. 18 (1966), 69-86. | Zbl 0223.10007

[026] [27] W. Ljunggren, New theorems concerning the diophantine equation x²+D=4yq, Acta Arith. 21 (1972), 183-191. | Zbl 0216.04101

[027] [28] L. J. Mordell, Diophantine Equations, Academic Press, London, 1969.

[028] [29] T. Nagell, Sur l'impossibilité de quelques équations à deux indéterminées, Norsk. Mat. Forensings Skrifter No. 13 (1923), 65-82.

[029] [30] T. Nagell, Løsning til oppgave nr 2, 1943, s. 29, Norske Mat. Tidsskrift 30 (1948), 62-64.

[030] [31] T. Nagell, Verallgemeinerung eines Fermatschen Satzes, Arch. Math. (Basel) 5 (1954), 153-159. | Zbl 0055.03608

[031] [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).

[032] [33] T. Nagell, On the Diophantine equation x²+8D=yⁿ, Ark. Mat. 3 (1954), 103-112.

[033] [34] S. Ramanujan, Question 464, J. Indian Math. Soc. 5 (1913), 120.

[034] [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. | Zbl 0371.10015

[035] [36] T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge University Press, Cambridge, 1986. | Zbl 0606.10011

[036] [37] B. M. E. Wren, y²+D=x⁵, Eureka 36 (1973), 37-38