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Numbers with "known" continued fractions

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#real-analysis #number-theory #irrational-numbers #continued-fractions #diophantine-approximation
3.6k
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In Search Of Elementary Proof Of Kobayashi's Theorem

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#number-theory #elementary-number-theory #prime-numbers #diophantine-approximation #geometry-of-numbers
236
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Bounding the norm of algebraic number of given degree and height

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#number-theory #diophantine-approximation
365
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Units in Cube Root System

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#algebra-precalculus #number-theory #diophantine-approximation
224
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Rational solutions of the system $ p^2-2 q^2 + r^2 =12, 2p^2 - 3 q^2 + s^2=42$?

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#number-theory #diophantine-equations #elliptic-curves #diophantine-approximation
215
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Rational solutions of quadratic Diophantine equation $ax^2+by^2+cz^2+du^2=v^2$?

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#number-theory #reference-request #diophantine-equations #elliptic-curves #diophantine-approximation
39
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Positive definite binary form of degree $\geq 3$, where $F(x,y)=m$ has finitely many solutions in $x,y\in\mathbb{Z}$

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#diophantine-approximation
57
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proving $\big \lfloor xn-\frac 1n \big\rfloor\neq \big\lfloor xn+\frac 1n\big\rfloor$

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#real-numbers #integers #ceiling-and-floor-functions #diophantine-approximation
102
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Equivalent to Roth's theorem

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#number-theory #inequality #diophantine-approximation
45
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Binary recurrence sequence in $\mathbb{Z}$

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#sequences-and-series #number-theory #diophantine-approximation
93
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Roth's theorem for $m$ algebraic numbers

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#number-theory #inequality #diophantine-approximation
129
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Bounding the height of an algebraic number in terms of height of the free coefficient in its minimal polynomial.

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#number-theory #algebraic-number-theory #diophantine-approximation
80
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Comparison between height of polynomial and height of coefficients of polynomial

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#number-theory #field-theory #algebraic-number-theory #arithmetic-geometry #diophantine-approximation
24
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Is this $2^{\lceil\log_2 d\rceil}$ inequality true?

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#diophantine-approximation
48
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Bad approximation by fractions with quadratic denominators

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#number-theory #diophantine-approximation

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