List questions from diophantine-equations

Published on 08 Dec 2018 - 9:38

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Find all positive integers $a$ and $b$ such that $(1 + a)(8 + b)(a + b) = 27ab$.

Published on 08 Dec 2018 - 18:01

496

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Pythagorean like Diophantine Equation

Published on 25 Mar 2026 - 19:01

374

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Solutions to $a,\ b,\ c,\ \frac{a}{b}+\frac{b}{c}+\frac{c}{a},\ \frac{b}{a} + \frac{c}{b} + \frac{a}{c} \in \mathbb{Z}$

Published on 27 Mar 2026 - 3:44

58

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Is this Diophantine problem solvable without invoking Fermat's Last Theorem?

Published on 10 Dec 2018 - 15:39

60

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Finding a subspace of dimension $3$ which does not intersect a rational subspace of dimension $2$

Published on 25 Mar 2026 - 23:16

199

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Find all values of $n$ such that $\varphi(n) = n/6$.

Published on 26 Mar 2026 - 1:11

227

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Find all positive integer $m$ such $2^{m}+1\mid5^m-1$

Published on 27 Mar 2026 - 7:14

171

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Are Transitions in a Hydrogen Atom Unique

Published on 27 Mar 2026 - 3:49

106

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Can $3^x=2y^2-1$ be solved over the natural numbers?

Published on 14 Dec 2018 - 6:47

481

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Find all Pythagorean triples $x^2+y^2=z^2$ where $x=21$

Published on 25 Mar 2026 - 19:06

148

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Determine number of all $\left\{P,Q,R,k \right\}$, such that $P_{(2k)}-Q_{(k)}=(R_{(k)})^2$

Published on 16 Dec 2018 - 23:51

1.9k

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What are the positive integer solutions to $x^2-x+1 = y^3$?

Published on 19 Mar 2026 - 16:27

186

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How can we solve the diophantine equation?

Published on 17 Dec 2018 - 22:10

895

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Prove that for any integer value of D, the equation 27x + 14y = D has integer solutions for x and y.

Published on 18 Dec 2018 - 7:22

List Question

Integer equations

Find all positive integers $a$ and $b$ such that $(1 + a)(8 + b)(a + b) = 27ab$.

Pythagorean like Diophantine Equation

Solutions to $a,\ b,\ c,\ \frac{a}{b}+\frac{b}{c}+\frac{c}{a},\ \frac{b}{a} + \frac{c}{b} + \frac{a}{c} \in \mathbb{Z}$

Is this Diophantine problem solvable without invoking Fermat's Last Theorem?

Finding a subspace of dimension $3$ which does not intersect a rational subspace of dimension $2$

Find all values of $n$ such that $\varphi(n) = n/6$.

Find all positive integer $m$ such $2^{m}+1\mid5^m-1$

Are Transitions in a Hydrogen Atom Unique

Can $3^x=2y^2-1$ be solved over the natural numbers?

Find all Pythagorean triples $x^2+y^2=z^2$ where $x=21$

Determine number of all $\left\{P,Q,R,k \right\}$, such that $P_{(2k)}-Q_{(k)}=(R_{(k)})^2$

What are the positive integer solutions to $x^2-x+1 = y^3$?

How can we solve the diophantine equation?

Prove that for any integer value of D, the equation 27x + 14y = D has integer solutions for x and y.

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