Question

$L^1$ and $L^4$ norm relation to fixed $L^2$ norm

score 80 · Answer 1 · 2024-01-28 03:36:06

80

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$L^1$ and $L^4$ norm relation to fixed $L^2$ norm

Published on 28 Jan 2024 - 3:36

score 170 · Answer 2 · 2024-02-15 18:44:40

170

Views

Writing 2024 as the sum of 3 and 4 squares

Published on 15 Feb 2024 - 18:44

score 64 · Answer 3 · 2024-02-15 20:57:58

64

Views

Sequence of squares which can't be written as the sum of a smaller non-zero square and twice a triangular number

Published on 15 Feb 2024 - 20:57

score 86 · Answer 4 · 2024-02-18 12:06:49

86

Views

Consequence following from the hypothesis $ : 7$ divides $a^2 + b^2$ with $ a, b \in \mathbb Z$

Published on 18 Feb 2024 - 12:06

score 63 · Answer 5 · 2024-03-24 01:47:38

63

Views

Integers that are sums of two squares

Published on 24 Mar 2024 - 1:47

score 55 · Answer 6 · 2015-01-03 16:38:47

55

Views

Prove by induction that $\sum_{k=0}^{n}(-1)^{n+k} k^{2} = \frac{n(n+1)}{2}$

Published on 03 Jan 2015 - 16:38

score 1.3k · Answer 7 · 2015-01-10 13:57:59

1.3k

Views

Numbers that are the sum of the squares of their prime factors

Published on 10 Jan 2015 - 13:57

score 621 · Answer 8 · 2026-03-27 07:47:34

621

Views

Pythagorean triples

Published on 27 Mar 2026 - 7:47

score 153 · Answer 9 · 2015-01-20 11:53:46

153

Views

Applying iterated function on the sum of the squares of the prime factors of $30$

Published on 20 Jan 2015 - 11:53

score 348 · Answer 10 · 2015-01-23 18:51:12

348

Views

Sum of two squares - Number of steps in Fermat descent

Published on 23 Jan 2015 - 18:51

score 390 · Answer 11 · 2026-03-25 17:26:05

390

Views

Integer solutions to $\prod\limits_{i=1}^{n}x_i=\sum\limits_{i=1}^{n}x_i^2$

Published on 25 Mar 2026 - 17:26

score 123 · Answer 12 · 2015-02-02 13:48:04

123

Views

Reduce $(a+b)^2(c+d)^2-16abcd$ to sum of squares

Published on 02 Feb 2015 - 13:48

score 148 · Answer 13 · 2015-02-09 03:45:30

148

Views

Let $F$ be a field in which we have elements satisfying $a^2+b^2+c^2 = −1$. Show that there exist elements satisfying $d^2+e^2 = −1$.

Published on 09 Feb 2015 - 3:45

score 91 · Answer 14 · 2015-02-09 04:33:56

91

Views

Let $F$ be a field and let $a,b,c,d\in F\Rightarrow (a^2+b^2)(c^2+d^2)$ can be written as $x^2+y^2$ for some $x,y\in F$?

Published on 09 Feb 2015 - 4:33

score 61 · Answer 15 · 2015-02-22 10:56:30

61

Views

Can sum of 3 composite squares be a perfect square?

Published on 22 Feb 2015 - 10:56

List Question

$L^1$ and $L^4$ norm relation to fixed $L^2$ norm

Writing 2024 as the sum of 3 and 4 squares

Sequence of squares which can't be written as the sum of a smaller non-zero square and twice a triangular number

Consequence following from the hypothesis $ : 7$ divides $a^2 + b^2$ with $ a, b \in \mathbb Z$

Integers that are sums of two squares

Prove by induction that $\sum_{k=0}^{n}(-1)^{n+k} k^{2} = \frac{n(n+1)}{2}$

Numbers that are the sum of the squares of their prime factors

Pythagorean triples

Applying iterated function on the sum of the squares of the prime factors of $30$

Sum of two squares - Number of steps in Fermat descent

Integer solutions to $\prod\limits_{i=1}^{n}x_i=\sum\limits_{i=1}^{n}x_i^2$

Reduce $(a+b)^2(c+d)^2-16abcd$ to sum of squares

Let $F$ be a field in which we have elements satisfying $a^2+b^2+c^2 = −1$. Show that there exist elements satisfying $d^2+e^2 = −1$.

Let $F$ be a field and let $a,b,c,d\in F\Rightarrow (a^2+b^2)(c^2+d^2)$ can be written as $x^2+y^2$ for some $x,y\in F$?

Can sum of 3 composite squares be a perfect square?

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