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

SZALAY, L., A note on the products of the terms of linear recurrences

52 László Szalay the absolute values of the integer coefficients of the logarithms in (16), we can choose B as B = x. So by (16) and Lemma 1 it follows that (17) Q > ec*(

l

oe™

l

o8 9+f). Combining (15) and (17) it yields the following inequality: (18) c

6x < c

7 ^logwlogg + ^ , and by (14) it follows that (19) c

6x < c

7 (log w log q + — log w ) < c

8 log w log q V c4 J with some c

8 > 0. Applying (14) again, we conclude that ^r<?log w < x and so by (19) (20) Cgq < log q follows. But (20) implies that q < qo, which proves the theorem. References [1] A. BAKER, A sharpening of the bounds for linear forms in logarithms II., Acta Arith. 24 (1973), 33-36. [2] P. KLSS, Pure powers and power classes in the recurrence sequences, Math. Slovaca 44 (1994), No. 5, 525-529. [3] K. LIPTAI. L. SZALAY, On products of the terms of linear recurrences, to appear. [4] A. PI: 1 HO, Perfect powers in second order linear recurrences, J. Num. Theory 15 (1982), 5-13. [5] A. PETHŐ, Perfect powers in second order linear recurrences, Topics in Classical Number Theory, Proceedings of the Conference in Budapest 1981, Colloq. Math. Soc. János Bolyai 34, North Holland, Amsterdam, 1217-1227.