Question

On the diophantine equation $xy=n(x+y)$ with $\gcd(x,y,n)=1$

score 164 · Answer 1 · 2026-04-15 12:07:29

164

Views

On the diophantine equation $xy=n(x+y)$ with $\gcd(x,y,n)=1$

Published on 15 Apr 2026 - 12:07

score 164 · Answer 2 · 2026-04-15 20:42:25

164

Views

Has the diophantine equation $xyz=n(x+y+z)$ for given $n\in \mathbb{N}$ only finitely many solutions $x,y,z\in \mathbb{N}$?

Published on 15 Apr 2026 - 20:42

score 177 · Answer 3 · 2026-04-16 15:50:55

177

Views

Find $(a^2+b^2),$ where $(a+b)=\dfrac{a}{b}+\dfrac{b}{a}$

Published on 16 Apr 2026 - 15:50

score 1.4k · Answer 4 · 2026-04-14 20:14:28

1.4k

Views

Find three numbers such that the sum of all three is a square and the sum of any two is a square

Published on 14 Apr 2026 - 20:14

score 210 · Answer 5 · 2026-03-26 04:30:12

210

Views

How to solve this linear Diophantine equation?

Published on 26 Mar 2026 - 4:30

score 375 · Answer 6 · 2026-04-17 05:33:25

375

Views

Find all solutions to $x^3+(x+1)^3+ \dots + (x+15)^3=y^3$

Published on 17 Apr 2026 - 5:33

score 106 · Answer 7 · 2026-04-16 00:54:12

106

Views

Cubic Diphantine equations of the form $Ax^3-By^3=C$.

Published on 16 Apr 2026 - 0:54

score 88 · Answer 8 · 2026-04-13 15:41:29

88

Views

How to solve this cubic Diophantine equation?

Published on 13 Apr 2026 - 15:41

score 413 · Answer 9 · 2026-04-10 17:32:24

413

Views

Determining number of integer solutions of Diophantine equation

Published on 10 Apr 2026 - 17:32

score 89 · Answer 10 · 2026-04-10 13:58:56

89

Views

Diophantine equation in $\mathbb{Z_+}$

Published on 10 Apr 2026 - 13:58

score 159 · Answer 11 · 2026-04-14 20:59:34

159

Views

Argument for why $a^2 + 1$ is never divisible by a $3 \mod 4$ integer

Published on 14 Apr 2026 - 20:59

score 98 · Answer 12 · 2026-04-16 14:14:13

98

Views

Solve Diophantine equation: $xy+5y=2x+(y+2)^2$

Published on 16 Apr 2026 - 14:14

score 144 · Answer 13 · 2026-04-15 10:25:30

144

Views

Given a fixed prime number $p$ and fixed positive integers $a$ and $k$; Find all positive integers $n$ such that $p^k \mid a^n-1$

Published on 15 Apr 2026 - 10:25

score 272 · Answer 14 · 2026-04-16 12:30:30

272

Views

Given prime $p$, for any integer $a$, exist integer $x,y$ such that $p\mid y^2+x^3+a$.

Published on 16 Apr 2026 - 12:30

score 344 · Answer 15 · 2026-03-26 04:28:31

344

Views

On largest box not containing integer vector solutions

Published on 26 Mar 2026 - 4:28

List Question

On the diophantine equation $xy=n(x+y)$ with $\gcd(x,y,n)=1$

Has the diophantine equation $xyz=n(x+y+z)$ for given $n\in \mathbb{N}$ only finitely many solutions $x,y,z\in \mathbb{N}$?

Find $(a^2+b^2),$ where $(a+b)=\dfrac{a}{b}+\dfrac{b}{a}$

Find three numbers such that the sum of all three is a square and the sum of any two is a square

How to solve this linear Diophantine equation?

Find all solutions to $x^3+(x+1)^3+ \dots + (x+15)^3=y^3$

Cubic Diphantine equations of the form $Ax^3-By^3=C$.

How to solve this cubic Diophantine equation?

Determining number of integer solutions of Diophantine equation

Diophantine equation in $\mathbb{Z_+}$

Argument for why $a^2 + 1$ is never divisible by a $3 \mod 4$ integer

Solve Diophantine equation: $xy+5y=2x+(y+2)^2$

Given a fixed prime number $p$ and fixed positive integers $a$ and $k$; Find all positive integers $n$ such that $p^k \mid a^n-1$

Given prime $p$, for any integer $a$, exist integer $x,y$ such that $p\mid y^2+x^3+a$.

On largest box not containing integer vector solutions

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