Question

System of Diophantine equations $a^2+b^2=2x^2+1,c^2+d^2=2y^2+1,ac-bd=1$ has no natural solutions.

score 233 · Answer 1 · 2018-07-14 14:51:48

233

Views

System of Diophantine equations $a^2+b^2=2x^2+1,c^2+d^2=2y^2+1,ac-bd=1$ has no natural solutions.

Published on 14 Jul 2018 - 14:51

score 143 · Answer 2 · 2018-07-17 22:20:43

143

Views

Diophantine with non-zero solutions

Published on 17 Jul 2018 - 22:20

score 293 · Answer 3 · 2018-07-20 02:01:15

293

Views

number of different ways to represent a positive integer as a binomial coefficient

Published on 20 Jul 2018 - 2:01

score 57 · Answer 4 · 2026-03-25 04:40:10

57

Views

Solving OR bounding sums of solutions to certain linear diophantine equations

Published on 25 Mar 2026 - 4:40

score 288 · Answer 5 · 2018-07-20 23:04:26

288

Views

triangles in $\mathbb{R}^n$ with all vertices in $\mathbb{Q}^n$

Published on 20 Jul 2018 - 23:04

score 780 · Answer 6 · 2018-07-21 17:24:00

780

Views

Parameterization to the Diophantine equation $x^2+4y^2=5z^2$

Published on 21 Jul 2018 - 17:24

score 198 · Answer 7 · 2026-03-23 16:29:08

198

Views

The diophantine equation $5\times 2^{x-4}=3^y-1$

Published on 23 Mar 2026 - 16:29

score 221 · Answer 8 · 2018-07-23 11:02:36

221

Views

If $ab \mid c(c^2-c+1)$ and $c^2+1 \mid a+b$ then prove that $\{a, b\}=\{c, c^2-c+1 \}$

Published on 23 Jul 2018 - 11:02

score 911 · Answer 9 · 2018-07-24 09:36:29

911

Views

Solve $\frac{1}{x}+\frac{1}{y}= \frac{1}{2007}$

Published on 24 Jul 2018 - 9:36

score 191 · Answer 10 · 2018-07-24 14:51:35

191

Views

Check whether $k \in [0, p]$ in the equation: ${a^k + b^k \equiv c^k}\mod{p}$ has no solutions under the following conditions

Published on 24 Jul 2018 - 14:51

score 302 · Answer 11 · 2018-07-24 16:53:54

302

Views

Finding solutions to the diophantine equation $xy(x+y) = n$.

Published on 24 Jul 2018 - 16:53

score 312 · Answer 12 · 2026-03-25 20:35:03

312

Views

Does this qualify as a prime-representing Diophantine equation?

Published on 25 Mar 2026 - 20:35

score 76 · Answer 13 · 2018-07-27 15:54:46

76

Views

Elementary solution to the diophantine equation $n(n+1)=4m(m+1)$?

Published on 27 Jul 2018 - 15:54

score 193 · Answer 14 · 2018-07-29 21:59:46

193

Views

Positive even numbered integer solutions of $y=n^2-m^2-x^2$

Published on 29 Jul 2018 - 21:59

score 202 · Answer 15 · 2026-03-25 04:35:38

202

Views

Why doesn't Buchberger's algorithm solve Hilbert's tenth problem?

Published on 25 Mar 2026 - 4:35

List Question

System of Diophantine equations $a^2+b^2=2x^2+1,c^2+d^2=2y^2+1,ac-bd=1$ has no natural solutions.

Diophantine with non-zero solutions

number of different ways to represent a positive integer as a binomial coefficient

Solving OR bounding sums of solutions to certain linear diophantine equations

triangles in $\mathbb{R}^n$ with all vertices in $\mathbb{Q}^n$

Parameterization to the Diophantine equation $x^2+4y^2=5z^2$

The diophantine equation $5\times 2^{x-4}=3^y-1$

If $ab \mid c(c^2-c+1)$ and $c^2+1 \mid a+b$ then prove that $\{a, b\}=\{c, c^2-c+1 \}$

Solve $\frac{1}{x}+\frac{1}{y}= \frac{1}{2007}$

Check whether $k \in [0, p]$ in the equation: ${a^k + b^k \equiv c^k}\mod{p}$ has no solutions under the following conditions

Finding solutions to the diophantine equation $xy(x+y) = n$.

Does this qualify as a prime-representing Diophantine equation?

Elementary solution to the diophantine equation $n(n+1)=4m(m+1)$?

Positive even numbered integer solutions of $y=n^2-m^2-x^2$

Why doesn't Buchberger's algorithm solve Hilbert's tenth problem?

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