On patterns occurring in binary algebraic numbers

Adamczewski, B.; Rampersad, N.

doi:10.1090/S0002-9939-08-09319-2

On patterns occurring in binary algebraic numbers
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by B. Adamczewski and N. Rampersad PDF

Proc. Amer. Math. Soc. 136 (2008), 3105-3109 Request permission

Abstract:

We prove that every algebraic number contains infinitely many occurrences of $7/3$-powers in its binary expansion. Using the same approach, we also show that every algebraic number contains either infinitely many occurrences of squares or infinitely many occurrences of one of the blocks $010$ or $02120$ in its ternary expansion.

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