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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

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

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

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.