RMC - Vol. 18 Num. 2, Florian Luca

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$% F. Luca, .121221222... is not quadratic, Rev. Mat. Complut. 18 (2005), no. 2, 353–362.%$

.121221222... Is Not Quadratic

Florian LUCA

Instituto de Matemáticas
Universidad Nacional Autónoma de México
C.P. 58180, Morelia, Michoacán — México

fluca@matmor.unam.mx

Received: July 30, 2004
Accepted: March 9, 2005

ABSTRACT

In this note, we show that if $b> 1$ is an integer, $f(X) (- Q[X]$ is an integer valued quadratic polynomial and $K > 0$ is any constant, then the $b$ -adic number

sum a bfn(n), n>0

where $an (- Z$ and $1< |an|< K$ for all $n> 0$ , is neither rational nor quadratic.

Key words: irrationality, applications of sieve methods.
2000 Mathematics Subject Classification: 11J72, 11N36.