List questions from diophantine-equations

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Strategies for solving rational Diophantine equations

Published on 22 Dec 2015 - 11:02

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Positive Integer solutions to $y = \frac{x z}{-x - z + x z}$

Published on 23 Dec 2015 - 5:28

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How to solve a diophantine equation pair?

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Integer solutions to $\frac{d^3}{r}+r=a^2$

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Solve for Rationals $p,q,r$ Satisfying $\frac{2p}{1+2p-p^2}+\frac{2q}{1+2q-q^2}+\frac{2r}{1+2r-r^2}=1$.

Published on 28 Mar 2026 - 1:15

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Describe the nonzero integer solutions to the equation $a^3 + b^3 + c^3 + d^3 + e^3 + f^3 + g^3 =0$

Published on 24 Dec 2015 - 20:48

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For any coprime integers $(x, y)$, $m\geq 2$, $\delta\geq 1$, is it true that $\mid x^m - y^{m+\delta} \mid \geq \delta$?

Published on 24 Dec 2015 - 21:46

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Find a example such $\frac{(x+y)^{x+y}(y+z)^{y+z}(x+z)^{x+z}}{x^{2x}y^{2y}z^{2z}}=2016$

Published on 25 Dec 2015 - 6:08

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Prove that $\gcd(k,n) = 1$ if and only if $ \exists m,d \in \mathbb{Z}: mk+nd=1$

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If $x-y = 5y^2 - 4x^2$, prove that $x-y$ is perfect square

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Describe the integral solutions to $y^2 = 12x^3 - 39$

Published on 26 Dec 2015 - 20:48

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Solve in set of natural numbers

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Describe the integral solutions to this cubic equation.

Published on 27 Dec 2015 - 16:52

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Rational points on $y^5 = x^4 + x^3 + x^2 + x + 1$

Published on 27 Dec 2015 - 21:58

List Question

Three pythagorean triples

Strategies for solving rational Diophantine equations

Positive Integer solutions to $y = \frac{x z}{-x - z + x z}$

How to solve a diophantine equation pair?

Integer solutions to $\frac{d^3}{r}+r=a^2$

Solve for Rationals $p,q,r$ Satisfying $\frac{2p}{1+2p-p^2}+\frac{2q}{1+2q-q^2}+\frac{2r}{1+2r-r^2}=1$.

Describe the nonzero integer solutions to the equation $a^3 + b^3 + c^3 + d^3 + e^3 + f^3 + g^3 =0$

For any coprime integers $(x, y)$, $m\geq 2$, $\delta\geq 1$, is it true that $\mid x^m - y^{m+\delta} \mid \geq \delta$?

Find a example such $\frac{(x+y)^{x+y}(y+z)^{y+z}(x+z)^{x+z}}{x^{2x}y^{2y}z^{2z}}=2016$

Prove that $\gcd(k,n) = 1$ if and only if $ \exists m,d \in \mathbb{Z}: mk+nd=1$

If $x-y = 5y^2 - 4x^2$, prove that $x-y$ is perfect square

Describe the integral solutions to $y^2 = 12x^3 - 39$

Solve in set of natural numbers

Describe the integral solutions to this cubic equation.

Rational points on $y^5 = x^4 + x^3 + x^2 + x + 1$

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