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$% F. Luca, .121221222... is not quadratic, Rev. Mat. Complut. 18 (2005), no. 2, 353–362.%$
.121221222... Is Not Quadratic
In this note, we show that if is an integer, is an integer valued quadratic polynomial and is any constant, then the -adic number
where and for all , is neither rational nor quadratic.
Key words: irrationality, applications of sieve methods.
2000 Mathematics Subject Classification: 11J72, 11N36.