Question

Non-linear system of equations over the positive integers — more unknowns than equations

score 208 · Answer 1 · 2026-03-25 03:07:52

208

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Non-linear system of equations over the positive integers — more unknowns than equations

Published on 25 Mar 2026 - 3:07

score 230 · Answer 2 · 2026-03-25 18:03:20

230

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$x^2-Dy^2=-1$ when D is square-free and has only prime divisors $\equiv 1 \mod 4$

Published on 25 Mar 2026 - 18:03

score 313 · Answer 3 · 2026-03-25 17:52:10

313

Views

Find all integers $x$ and $y$ for which $\frac{x^2}{x-1}+\frac{y^2}{y-1}$ is an integer.

Published on 25 Mar 2026 - 17:52

score 103 · Answer 4 · 2018-05-23 04:21:49

103

Views

Integer solutions to $x^y - y^x = 1$

Published on 23 May 2018 - 4:21

score 190 · Answer 5 · 2026-03-25 09:28:58

190

Views

Finishing the task to find the solutions of $\frac{1}{x}-\frac{1}{y}=\frac{1}{\varphi(xy)},$ where $\varphi(n)$ denotes the Euler's totient function

Published on 25 Mar 2026 - 9:28

score 83 · Answer 6 · 2018-05-27 01:20:06

83

Views

Does this:$(\cos x) ^{\frac{1}{\cos x}}+(\sin x) ^{\frac{1}{\sin x}}=1$ have integers solution?

Published on 27 May 2018 - 1:20

score 190 · Answer 7 · 2026-03-25 06:06:30

190

Views

$2^W = (2a_1+1)^2 \cdot 2^{M_1}-a_1$ - is there a nontrivial diophantine solution in $M_1,a_1$ given possible?

Published on 25 Mar 2026 - 6:06

score 34 · Answer 8 · 2026-03-25 23:35:21

34

Views

Will this equation ever have an positive integer value?

Published on 25 Mar 2026 - 23:35

score 367 · Answer 9 · 2018-06-01 06:33:29

367

Views

Which integers can be written as $x^2+2y^2-3z^2\ $?

Published on 01 Jun 2018 - 6:33

score 114 · Answer 10 · 2026-03-25 22:10:41

114

Views

Finish the exercise to find or count the solutions of the equation $n x^2-\operatorname{rad}(n)=y^3$ over positive integers

Published on 25 Mar 2026 - 22:10

score 52 · Answer 11 · 2018-06-04 08:11:47

52

Views

Diophantine trouble

Published on 04 Jun 2018 - 8:11

score 64 · Answer 12 · 2026-03-25 17:59:55

64

Views

On numbers of the form $\pm x^2\pm N_k$, with $x\geq 1$ integer and $N_k$ denoting primorials

Published on 25 Mar 2026 - 17:59

score 440 · Answer 13 · 2026-03-25 01:28:06

440

Views

On the complete rational solutions of $x^3+y^3+z^3=1$

Published on 25 Mar 2026 - 1:28

score 54 · Answer 14 · 2018-06-06 14:50:35

54

Views

Calculate number of solutions in $N$ of diophantine inequality using generating functions.

Published on 06 Jun 2018 - 14:50

score 89 · Answer 15 · 2026-03-20 10:59:18

89

Views

$\sum\limits_{\mathbb{d|n}}{f(d)}=\sum\limits_{\mathbb{d|n}}{g(d)}\implies f(n)=g(n)?$

Published on 20 Mar 2026 - 10:59

List Question

Non-linear system of equations over the positive integers — more unknowns than equations

$x^2-Dy^2=-1$ when D is square-free and has only prime divisors $\equiv 1 \mod 4$

Find all integers $x$ and $y$ for which $\frac{x^2}{x-1}+\frac{y^2}{y-1}$ is an integer.

Integer solutions to $x^y - y^x = 1$

Finishing the task to find the solutions of $\frac{1}{x}-\frac{1}{y}=\frac{1}{\varphi(xy)},$ where $\varphi(n)$ denotes the Euler's totient function

Does this:$(\cos x) ^{\frac{1}{\cos x}}+(\sin x) ^{\frac{1}{\sin x}}=1$ have integers solution?

$2^W = (2a_1+1)^2 \cdot 2^{M_1}-a_1$ - is there a nontrivial diophantine solution in $M_1,a_1$ given possible?

Will this equation ever have an positive integer value?

Which integers can be written as $x^2+2y^2-3z^2\ $?

Finish the exercise to find or count the solutions of the equation $n x^2-\operatorname{rad}(n)=y^3$ over positive integers

Diophantine trouble

On numbers of the form $\pm x^2\pm N_k$, with $x\geq 1$ integer and $N_k$ denoting primorials

On the complete rational solutions of $x^3+y^3+z^3=1$

Calculate number of solutions in $N$ of diophantine inequality using generating functions.

$\sum\limits_{\mathbb{d|n}}{f(d)}=\sum\limits_{\mathbb{d|n}}{g(d)}\implies f(n)=g(n)?$

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