On sums of $S$-units and linear recurrences

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1. [1] S. Chowla: Proof of a conjecture of Julia Robinson. Norske Vid. Selsk. Forh.(Trondheim) 34 (1961) 107-109. Zbl0105.02803MR142538
2. [2] E. Dubois and G. Rhin, Sur la majoration de formes linéaires a coefficients algébriques réels et p-adiques. Démonstration d'une conjecture de K. Mahler. C.R. Acad. Sc. Paris282, Série A-1211 (1976). Zbl0339.10031MR429783
3. [3] K. Gyory, On the number of solutions of linear equations in units of an algebraic number field. Comment. Math. Helv.54 (1979) 583-600. Zbl0437.12004MR552678
4. [4] S. Lang, Integral points on curves. Inst. Hautes Etudes Sci. Publ. Math. no.6 (1960) 27-43. Zbl0112.13402MR130219
5. [5] D.J. Lewis and K. Mahler, On the representation of integers by binary forms. Acta Arith.6 (1961) 333-363. Zbl0102.03601MR120195
6. [6] K. Mahler, Zur Approximation algebraischer Zahlen (I). Uber den gröszten Primteiler Binärer Formen. Math. Ann.107 (1933) 691-730. Zbl0006.10502MR1512822JFM59.0220.01
7. [7] K. Mahler: Math. Rev.42 (1971) 3028. 
8. [8] T. Nagell, Sur une propriété des unités d'un corps algébrique. Arkiv för Mat.5 (1965) 343-356. Zbl0128.03403MR190128
9. [9] T. Nagell: Quelques problèmes relatifs aux unités algébriques. Arkiv för Mat.8 (1969) 115-127. Zbl0213.06902MR268154
10. [10] T. Nagell: Sur un type particulier d'unités algébriques. Arkiv för Mat.8 (1969) 163-184. Zbl0213.06901MR268165
11. [11] M. Newman: Units in arithmetic progression in an algebraic number field. Proc. Amer. Math. Soc.43 (1974) 266-268. Zbl0285.12011MR330101
12. [12] G. Polya, Arithmetische Eigenschaften der Reihenentwicklungen. J. reine angew. Math. 151 (1921) 1-31. Zbl47.0276.02JFM47.0276.02
13. [13] A.J. Van Der Poorten, Some problems of recurrent interest. Macquarie Math. Reports; Macquarie Univ., Northride, Australia, 81-0037 (1981). 
14. [14] A.J. Van Der Poorten and H.P. Schlickewei, The growth conditions for recurrence sequences. Macquarie Math. Reports 82 -0041 (1982). 
15. [15] H.P. SchlickeweiÜber die diophantische Gleichung x 1+x2+...+xn=0Acta Arith. 33 (1977) 183-185. Zbl0355.10017MR439747
16. [16] H.P. Schlickewei: The p-adic Thue-Siegel-Roth-Schmidt Theorem. Arch Math.29 (1977) 267-270. Zbl0365.10026MR491529
17. [17] W.M. Schmidt: Simultaneous approximation to algebraic numbers by elements of a number fieldMonatsh. Math.79 (1975) 55-66. Zbl0317.10042MR364112
18. [18] W.M. Schmidt: Diophantine Approximation, Lecture Notes in Math. 785, Springer Verlag, Berlin Etc. 1980. Zbl0421.10019MR568710
19. [19] TH. Schneider: Anwendung eines abgeänderten Roth-Ridoutschen Satzes auf diophantische Gleichungen. Math. Ann.169 (1967) 177-182. Zbl0146.26904MR215792
20. [20] T.N. Shorey, Linear forms in numbers of a binary recursive sequence. Acta Arith, to appear. Zbl0491.10011

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