Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1997. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 24)

LIPTAI, K. and TÓMÁCS, T., Pure powers in recurrence sequences

Pure powers in recurrence sequences 39 with some C3, 04,05. Using (4) and (7) we get ceqlogw < x < c

5 log glog w, i.e. q < C7logg, where Cq and C7 are constants. But this inequality does not hold if q > g

0 = qo{G

, n, K

, A;), which proves the theorem. References [1] A. BAKER, A sharpening of the bounds for linear forms in logarithms II, Acta Arithm. 24 (1973), 33-36. [2] J. H. E. COHN, On square Fibonacci numbers, J. London Math. Soc. 39 (1964), 537-540. [3] J. H. E. COHN, Squares in some recurrent sequences, Pacific J. Math. 41 (1972), 631-646. [4] J. H. E. COHN, Eight Diophantine equations, Proc. London Math. Soc. 16 (1966), 153-166. [5] J. H. E. COHN

, Five Diophatine equations, Math. Scand. 21 (1967), 61-70. [6] P. KLSS, Pure powers and power classes in recurrence sequences, (to appear). [7] P. KLSS, Differences of the terms of linear recurrences, Studia Sei. Math. Hungar. 20 (1985), 285-293. [8] W. LJUNGGREN, Zur Theorie der Gleichung x

2 + 1 = Dy

4, Avh. Norske Vid Akad. Oslo 5 (1942). [9] J. LONDON and R. FINKELSTEIN

, On Fibonacci and Lucas numbers which are perfect powers, Fibonacci Quart. 7 (1969) 476-481, 487, errata ibid 8 (1970) 248. [10] J. LONDON and R. FINKELSTEIN, On Mordell's equation y

2-k = z

3, Bowling Green University Press (1973). [11] W. L. MCDANIEL and P. RLBENBOIM, Squares and double-squares in Lucas sequences, C. R. Math. Acad. Sei. Soc. R. Canada 14 (1992), 104-108. [12] A. PETHŐ, Full cubes in the Fibonacci sequence, Publ. Math. Debrecen 30 (1983), 117-127.