Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 2001. Sectio Mathematicae (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 28)
Kiss, P. & MÁTYÁS, F., On products and sums of the terms of linear recurrences
On products and sums of the terms of linear recurrences 9 that is, x but this is a contradiction if x > nTherefore the inequality (10) of the theorem holds with 0 < Co < C3 and no — max (nA 2 < ! < 6 Proof of Theorem 2. Using the estimation (19) x 1 I _ plog I a 1 1 1 log I «11 ^ gCio^i if Xi > 717, suppose that (20) I < p ClS? 1 with a suitable constant 0 < c\ < c 10 and sufficiently large xi. Using (4) for G {1 } and (3) for G® (2 < i < m), then (21) aiaí 1 1 + A* 3=a I i=2 j=l = a 1a x 1 1(l+e 1) for any x\ > , where |£i| < e Cl IC l, since > max (a^) and |cvi| > 2 <i<m any (i,j) /(1,1). From (20), by (19) and (21), we get that ,0') for a 1a 1 «T- (1+ei 3 C j X* x p ^ 1 1 < < I ai C* j 11 e^o^'i _ „(^-Cjo^! _ -< if X\ > 779. This implies the inequalities (22) Ci!^ 1 < 1+ \ £ l\ + ec» X l < 1 + e" if > 77-10. From this we can get |s| < laiorf 1! (1 + eCiaa? 1) < e c»*\
