Question

If $(a^2+b^2) \mid (c^2+d^2)$ and $\gcd(a,b)=\gcd(c,d)=1$ and $\gcd(a,c)>1$, what can be said about the components?

score 118 · Answer 1 · 2026-04-16 05:20:11

118

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If $(a^2+b^2) \mid (c^2+d^2)$ and $\gcd(a,b)=\gcd(c,d)=1$ and $\gcd(a,c)>1$, what can be said about the components?

Published on 16 Apr 2026 - 5:20

score 123 · Answer 2 · 2026-04-13 07:26:51

123

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Geometric interpretation of linear forms in the sum of four (or eight) squares identity

Published on 13 Apr 2026 - 7:26

score 1.5k · Answer 3 · 2026-04-15 04:47:33

1.5k

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Prove that $x^2 + y^2 = 3(z^2 + m^2)$ has no solutions in integer

Published on 15 Apr 2026 - 4:47

score 1.9k · Answer 4 · 2026-04-12 03:46:34

1.9k

Views

how can i calculate square sum of all the products of the summation?

Published on 12 Apr 2026 - 3:46

score 5.1k · Answer 5 · 2026-04-12 03:48:46

5.1k

Views

Supposed $a,b \in \mathbb{Z}$. If $ab$ is odd, then $a^{2} + b^{2}$ is even.

Published on 12 Apr 2026 - 3:48

score 199 · Answer 6 · 2026-04-12 15:06:47

199

Views

When $Ax^2+By^2=z^2$ has a solution in integers?

Published on 12 Apr 2026 - 15:06

score 145 · Answer 7 · 2026-04-11 06:32:16

145

Views

Are there no even squares expressible as the sum of two prime squares?

Published on 11 Apr 2026 - 6:32

score 1.9k · Answer 8 · 2026-04-29 12:51:52

1.9k

Views

Numbers as sum of distinct squares

Published on 29 Apr 2026 - 12:51

score 103 · Answer 9 · 2026-04-16 17:11:32

103

Views

Prove $\forall n\in\mathbb{N}, \exists m\in\mathbb{N}; n=\pm1^2\pm2^2\pm\cdots\pm m^2.$

Published on 16 Apr 2026 - 17:11

score 2.8k · Answer 10 · 2026-04-10 09:21:43

2.8k

Views

Numbers which are not the sum of distinct squares

Published on 10 Apr 2026 - 9:21

score 270 · Answer 11 · 2026-04-15 02:56:59

270

Views

How can I solve $m^2+n^2=5077$

Published on 15 Apr 2026 - 2:56

score 1k · Answer 12 · 2026-04-10 10:17:30

1k

Views

How to show a number is not a sum of three squares

Published on 10 Apr 2026 - 10:17

score 403 · Answer 13 · 2026-04-14 14:06:13

Why is there a pattern for making orders of perfect squares (first one, second one, third one) by simply adding two to the next adding each time?

score 1.3k · Answer 14 · 2026-04-12 14:27:08

1.3k

Views

Which integers are a sum of two relatively prime squares?

Published on 12 Apr 2026 - 14:27

score 158 · Answer 15 · 2026-04-13 15:49:32

158

Views

Application of the Jacobian

Published on 13 Apr 2026 - 15:49

List Question

If $(a^2+b^2) \mid (c^2+d^2)$ and $\gcd(a,b)=\gcd(c,d)=1$ and $\gcd(a,c)>1$, what can be said about the components?

Geometric interpretation of linear forms in the sum of four (or eight) squares identity

Prove that $x^2 + y^2 = 3(z^2 + m^2)$ has no solutions in integer

how can i calculate square sum of all the products of the summation?

Supposed $a,b \in \mathbb{Z}$. If $ab$ is odd, then $a^{2} + b^{2}$ is even.

When $Ax^2+By^2=z^2$ has a solution in integers?

Are there no even squares expressible as the sum of two prime squares?

Numbers as sum of distinct squares

Prove $\forall n\in\mathbb{N}, \exists m\in\mathbb{N}; n=\pm1^2\pm2^2\pm\cdots\pm m^2.$

Numbers which are not the sum of distinct squares

How can I solve $m^2+n^2=5077$

How to show a number is not a sum of three squares

Why is there a pattern for making orders of perfect squares (first one, second one, third one) by simply adding two to the next adding each time?

Which integers are a sum of two relatively prime squares?

Application of the Jacobian

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