Question

How is the Pell-like equation $ax^2-by^2 = c$ solved?

score 430 · Answer 1 · 2026-04-13 19:41:42

430

Views

How is the Pell-like equation $ax^2-by^2 = c$ solved?

Published on 13 Apr 2026 - 19:41

score 69 · Answer 2 · 2026-04-15 20:42:25

69

Views

Let $w<x$ be integers with $x^2-w^2$ beeing a square. If no $y$ exists with $y^2-x^2$, $y^2-w^2$ being squares, can we show no $y$ exists for $nw<nx$?

Published on 15 Apr 2026 - 20:42

score 112 · Answer 3 · 2026-04-14 16:00:08

112

Views

Solution to Pell's equation $a^2 - Nb^2 = 1$ when $a$ is an even integer

Published on 14 Apr 2026 - 16:00

score 98 · Answer 4 · 2026-04-13 20:37:29

98

Views

Writing an integer $m$ as the sum of $2m$ integers contained in $[-2,2] \cap \mathbb Z$

Published on 13 Apr 2026 - 20:37

score 136 · Answer 5 · 2026-04-13 23:26:38

136

Views

Is there any solutions to the diophantine equation $x^2 + y^2 = 2z^3, x \neq y$?

Published on 13 Apr 2026 - 23:26

score 152 · Answer 6 · 2026-04-17 08:56:47

152

Views

On relation between prime numbers and exponential Diophantine equation $c\cdot a^x\pm b=z$, feat. $71999999\cdots$

Published on 17 Apr 2026 - 8:56

score 197 · Answer 7 · 2026-04-16 02:30:23

197

Views

Find all integers $x,y$ such that $x^5-x^3-x^2+1=y^2$

Published on 16 Apr 2026 - 2:30

score 55 · Answer 8 · 2026-04-14 03:34:53

55

Views

Solving the exponential Diophantine equation $2^{m+1} = zk + 1$ where $m,k,z \in Z$ for a given very large $z$

Published on 14 Apr 2026 - 3:34

score 1.8k · Answer 9 · 2026-04-12 09:31:26

1.8k

Views

Is there any variation known to the sum of two squares theorem?

Published on 12 Apr 2026 - 9:31

score 150 · Answer 10 · 2026-04-16 12:04:51

150

Views

Finding all integers $m$ and $n$ satisfying $\frac{1}{m}-\frac{1}{n}=\frac{1}{100}$

Published on 16 Apr 2026 - 12:04

score 41 · Answer 11 · 2026-04-11 04:09:24

41

Views

How to recover a matrix with "linear" entries from its homogenous characteristic polynomial?

Published on 11 Apr 2026 - 4:09

score 54 · Answer 12 · 2026-04-09 00:50:35

54

Views

About a quartic diophantine equation in several variables

Published on 09 Apr 2026 - 0:50

score 112 · Answer 13 · 2026-04-13 21:31:05

112

Views

Prove that a Diophantine equation $ax^3 + by^2 = c$ has or doesn't have integer solutions

Published on 13 Apr 2026 - 21:31

score 185 · Answer 14 · 2026-04-16 02:59:37

185

Views

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

Published on 16 Apr 2026 - 2:59

score 50 · Answer 15 · 2026-04-11 04:17:04

50

Views

A Diophantine equation along with an inequality

Published on 11 Apr 2026 - 4:17

List Question

How is the Pell-like equation $ax^2-by^2 = c$ solved?

Let $w<x$ be integers with $x^2-w^2$ beeing a square. If no $y$ exists with $y^2-x^2$, $y^2-w^2$ being squares, can we show no $y$ exists for $nw<nx$?

Solution to Pell's equation $a^2 - Nb^2 = 1$ when $a$ is an even integer

Writing an integer $m$ as the sum of $2m$ integers contained in $[-2,2] \cap \mathbb Z$

Is there any solutions to the diophantine equation $x^2 + y^2 = 2z^3, x \neq y$?

On relation between prime numbers and exponential Diophantine equation $c\cdot a^x\pm b=z$, feat. $71999999\cdots$

Find all integers $x,y$ such that $x^5-x^3-x^2+1=y^2$

Solving the exponential Diophantine equation $2^{m+1} = zk + 1$ where $m,k,z \in Z$ for a given very large $z$

Is there any variation known to the sum of two squares theorem?

Finding all integers $m$ and $n$ satisfying $\frac{1}{m}-\frac{1}{n}=\frac{1}{100}$

How to recover a matrix with "linear" entries from its homogenous characteristic polynomial?

About a quartic diophantine equation in several variables

Prove that a Diophantine equation $ax^3 + by^2 = c$ has or doesn't have integer solutions

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

A Diophantine equation along with an inequality

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