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Seva
Seva
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Chebyshev Chebyshev's Theorem

Hi, 

I´m looking for Chebyshev´s theorem which speaks ofsays that the following inequality $|x(k)-y|<3/k$ has infinitely many solutions, where $x(k)=x_0+k\alpha (mod 1)$$x(k)=x_0+k\alpha \pmod 1$, $\alpha$ is an irrational number, and $x_0,y\in S^{1}$$x_0,y\in S^1$. AnyoneDoes anybody know, what the correctexact formulation of this theorem?

Chebyshev Theorem

Hi, I´m looking Chebyshev´s theorem which speaks of the following inequality $|x(k)-y|<3/k$ has infinitely many solutions, where $x(k)=x_0+k\alpha (mod 1)$, $\alpha$ is an irrational number, $x_0,y\in S^{1}$. Anyone know, what the correct formulation of this theorem?

Chebyshev's Theorem

Hi, 

I´m looking for Chebyshev´s theorem which says that the inequality $|x(k)-y|<3/k$ has infinitely many solutions, where $x(k)=x_0+k\alpha \pmod 1$, $\alpha$ is an irrational number, and $x_0,y\in S^1$. Does anybody know the exact formulation?

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Rosendo
Rosendo
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Chebyshev Theorem

Hi, I´m looking Chebyshev´s theorem which speaks of the following inequality $|x(k)-y|<3/k$ has infinitely many solutions, where $x(k)=x_0+k\alpha (mod 1)$, $\alpha$ is an irrational number, $x_0,y\in S^{1}$. Anyone know, what the correct formulation of this theorem?