On the diophantine equation $D₁x²+D₂=2^{n+2}$

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1. [1] R. Apéry, Sur une équation diophantienne, C. R. Acad. Sci. Paris Sér. A 251 (1960), 1263-1264. Zbl0093.04703
2. [2] A. Baker, Contribution to the theory of diophantine equations I: On the representation of integers by binary forms, Philos. Trans. Roy. Soc. London Ser. A 263 (1967), 273-297. 
3. [3] V. I. Baulin, On an indeterminate equation of the third degree with least positive discriminant, Tul'sk. Gos. Ped. Inst. Uchen. Zap. Fiz.-Mat. Nauk Vyp. 7 (1960), 138-170 (in Russian). 
4. [4] E. Bender and N. Herzberg, Some diophantine equations related to the quadratic form ax²+by², in: Studies in Algebra and Number Theory, G.-C. Rota (ed.), Adv. in Math. Suppl. Stud. 6, Academic Press, San Diego 1979, 219-272. 
5. [5] F. Beukers, On the generalized Ramanujan-Nagell equation I, Acta Arith. 38 (1981), 389-410. Zbl0371.10014
6. [6] J. H. E. Cohn, On square Fibonacci numbers, J. London Math. Soc. 39 (1964), 537-540. Zbl0127.26705
7. [7] K. Győry and Z. Z. Papp, Norm form equations and explicit lower bounds for linear forms with algebraic coefficients, in: Studies in Pure Mathematics, Akadémiai Kiadó, Budapest 1983, 245-257. Zbl0518.10020
8. [8] M.-H. Le, The divisibility of the class number for a class of imaginary quadratic fields, Kexue Tongbao (Chinese) 32 (1987), 724-727 (in Chinese). 
9. [9] M.-H. Le, On the number of solutions of the generalized Ramanujan-Nagell equation $x²-D=2^n+2$, Acta Arith. 60 (1991), 149-167. 
10. [10] R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, Reading, Mass., 1983. 
11. [11] M. Mignotte and M. Waldschmidt, Linear forms in two logarithms and Schneider's method III, Ann. Fac. Sci. Toulouse 97 (1989), 43-75. Zbl0702.11044
12. [12] T. Nagell, The diophantine equation $x²+7=2^n$, Ark. Mat. 4 (1960), 185-187 Zbl0103.03001