Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1998. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 25)

ZAY , B., An application of the continued fractions for ... in solving some types of Pell's equations

14 Béla Zay K - DK

2

n = (-l)

n+

1 = (-l)

n_

1c

n

+i, (that is c

n+

1 = 1 for any n). References [1] D. E. FERGUSON, Letter to the editor, Fibonacci Quart., 8 (1970), 88-89. [2] V. E. HOGATT JR., and M. BICKNELL-JOHNSON, A primer for the Fibonacci numbers XVII: Generalized Fibonacci numbers satisfying U

n + 1 U

n-1 —U* = ±1

, Fibonacci Quart., 2 (1978), 130-137. [3] P. Kiss, On second order recurrences and continued fractions, Bull. Malaysian Math. Soc. (2) 5 (1982) 33-41. [4] K. LIPTAI

, On a Diophantine problem, Discuss. Math., (to appear). [5] I. NIVEN, H. S. ZUCKERMAN, An introduction to the theory of numbers, John Wiley and Sons, London • New York, 1960. [6] VV. SIERPINSKI, Elementary Theory of Numbers, PWN-Polish Scientific Publishers, Warszawa, 1987. BÉLA ZAY KÁROLY ESZTERHÁZY TEACHERS' TRAINING COLLEGE DEPARTMENT OF MATHEMATICS H-3301 EGER, PF. 43 HUNGARY