List questions from vieta-jumping

Published on 19 Dec 2017 - 12:38

750

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Prove that two polynomials are constants if $P(x^2+x+1)=Q(x^2-x+1)$

Published on 03 Jan 2018 - 16:18

4.2k

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Let $x$ and $y$ be positive integers such that $xy \mid x^2+y^2+1$.

Published on 01 Mar 2012 - 14:13

3.7k

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Proving there are an infinite number of pairs of positive integers $(m,n)$ such that $\frac{m+1}{n}+\frac{n+1}{m}$ is a positive integer

Published on 30 May 2012 - 12:00

480

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Find infinitely many pairs of integers $a$ and $b$ with $1 < a < b$, so that $ab$ exactly divides $a^2 +b^2 −1$.

Published on 28 Jan 2013 - 5:27

1.6k

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Resource for Vieta root jumping

Published on 28 Jan 2013 - 6:35

1.1k

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Divisibility - Math Olympiad: $x|(y^2+m)$ and $y|(x^2+m) $

Published on 15 Mar 2013 - 21:47

163

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Infinitely many solutions of the equation $\frac{x+1}{y}+\frac{y+1}{x} = 4$

Published on 04 Sep 2020 - 18:20

173

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A Diophantine Equation Related to the Markoff Numbers

Published on 17 Dec 2020 - 15:29

312

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A caboodle of Pell's equation in one? $x^2+y^2-5xy+5=0$

Published on 19 Jan 2021 - 17:02

97

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Are all the solutions produced by Mathematica?

Published on 18 Mar 2021 - 11:50

1.5k

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Uses of Vieta Jumping in research mathematics?

Published on 22 Apr 2021 - 14:31

247

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If $x^2 - 10ax - 11b = 0$ has roots $c$ and $d$ and $x^2 - 10cx - 11d = 0$ has roots $a$ and $b$, then find $a + b + c + d$?

Published on 31 May 2021 - 9:49

162

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Understanding vieta jumping.

Published on 01 Jun 2022 - 14:37

80

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Finding the positive integer of $\frac{a^2+b^2}{ab+1}$ without Vieta-Jumping

Published on 26 Jun 2022 - 0:05

List Question

Equation with integers $x$, $y$

Prove that two polynomials are constants if $P(x^2+x+1)=Q(x^2-x+1)$

Let $x$ and $y$ be positive integers such that $xy \mid x^2+y^2+1$.

Proving there are an infinite number of pairs of positive integers $(m,n)$ such that $\frac{m+1}{n}+\frac{n+1}{m}$ is a positive integer

Find infinitely many pairs of integers $a$ and $b$ with $1 < a < b$, so that $ab$ exactly divides $a^2 +b^2 −1$.

Resource for Vieta root jumping

Divisibility - Math Olympiad: $x|(y^2+m)$ and $y|(x^2+m) $

Infinitely many solutions of the equation $\frac{x+1}{y}+\frac{y+1}{x} = 4$

A Diophantine Equation Related to the Markoff Numbers

A caboodle of Pell's equation in one? $x^2+y^2-5xy+5=0$

Are all the solutions produced by Mathematica?

Uses of Vieta Jumping in research mathematics?

If $x^2 - 10ax - 11b = 0$ has roots $c$ and $d$ and $x^2 - 10cx - 11d = 0$ has roots $a$ and $b$, then find $a + b + c + d$?

Understanding vieta jumping.

Finding the positive integer of $\frac{a^2+b^2}{ab+1}$ without Vieta-Jumping

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