Az Egri Ho Si Minh Tanárképző Főiskola Tud. Közleményei. 1987. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 18/11)

Bogdan Tropak: Some algebraic properties of linear recurrences

- 78 Suppose that, by above condition gCx5 is irreducible. Then g> CcO ß* 0 For any a. being a root- or gCx). Put. K :. = I (x - aj aj , where a^ are roots of gCx). First- of all we see that X^ has a form a.x + b. with rational a,b . Thus we have J J C10> (x) with not constant u and u l 2 On the other hand we have F,(*o>--"

xic-i) - n J S

i Ca )X, 4 t x. t -1 But 2 «t(<OHi>r - Hi) 2 c.K»-' if if i = j = / 0 \ g> Ca. )(x-a. ) L I k k hence k t = i r = 1 and from this it follows that k F

g(

xo> — >

xk-J - n [*-<\Kh] - a i=i with a rational A NU what common with CIO) gives a contradiction to the assumption on gCx> This contradiction completes the proof.