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Autor:
Hančl, Jaroslav, Nguyen, Tho Phuoc
In 1974, M. B. Nathanson proved that every irrational number $\alpha$ represented by a simple continued fraction with infinitely many elements greater than or equal to $k$ is approximable by an infinite number of rational numbers $p/q$ satisfying $|\
Externí odkaz:
http://arxiv.org/abs/2407.11525
Autor:
Hančl, Jaroslav, Nguyen, Tho Phuoc
Legendre's theorem states that every irreducible fraction $\frac{p}{q}$ which satisfies the inequality $\left |\alpha-\frac{p}{q} \right | < \frac{1}{2q^2}$ is convergent to $\alpha$. Later Barbolosi and Jager improved this theorem. In this paper we
Externí odkaz:
http://arxiv.org/abs/2407.11166