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Answers.
Answers.

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On the expansions of a real number to several integer bases Yann

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... drawn from small intervals by finding a correspondence between Zeckendorf decompositions in the interval [m, m + Fα(n) ) and in the interval [0, Fα(n) ) when a certain gentle condition is placed on the integers m we consider. The key step was to show that almost surely an integer m chosen uniformly ...
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Vincent's theorem

In mathematics, Vincent's theorem—named after Alexandre Joseph Hidulphe Vincent—is a theorem that isolates the real roots of polynomials with rational coefficients.Even though Vincent's theorem is the basis of the fastest method for the isolation of the real roots of polynomials, it was almost totally forgotten, having been overshadowed by Sturm's theorem; consequently, it does not appear in any of the classical books on the theory of equations (of the 20th century), except for Uspensky's book. Two variants of this theorem are presented, along with several (continued fractions and bisection) real root isolation methods derived from them.
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