## Continued fractional algebraic independence of sequences.(English)Zbl 0862.11045

A theorem of P. Bundschuh [Osaka J. Math. 25, 849-858 (1988; Zbl 0712.11041)] is used to derive a criterion that $$k$$ sequences $$(a_{in})_n$$, $$1\leq i\leq k$$, of positive real numbers are continued fractional algebraically independent. This means, by definition, that for every sequence $$(c_n)_n$$ of positive integers, the continued fractions $$[a_{i1}c_1, a_{i2} c_2, \dots]$$ are algebraically independent for $$1\leq i\leq k$$.

### MSC:

 11J70 Continued fractions and generalizations 11J71 Distribution modulo one

### Keywords:

continued fractions; algebraic independence

Zbl 0712.11041