Question

Solving $x^2 + y^2 = M$ over integers

score 388 · Answer 1 · 2020-01-12 13:30:33

388

Views

Solving $x^2 + y^2 = M$ over integers

Published on 12 Jan 2020 - 13:30

score 126 · Answer 2 · 2020-01-12 17:48:24

126

Views

Solving $x^2 + y^2 = M$ with $M$ prime

Published on 12 Jan 2020 - 17:48

score 110 · Answer 3 · 2020-01-20 08:30:43

110

Views

Knowing $2017 = 9^2 + 44^2$. find $m,n$ which satisfy $2017^2 = m^2 + n^2$

Published on 20 Jan 2020 - 8:30

score 151 · Answer 4 · 2026-03-25 13:58:10

151

Views

Find the asymptotic expansion as $N \rightarrow \infty$ of $\sum_{k=1}^{\left\lfloor{N/2}\right\rfloor} \left\{{\sqrt{{N}^{2}+{k}^{2}}}\right\}$

Published on 25 Mar 2026 - 13:58

score 168 · Answer 5 · 2020-01-21 07:32:22

168

Views

Prove that $A^2=a_1^2+a_2^2-a_3^2-a_4^2$ for all integers $A$.

Published on 21 Jan 2020 - 7:32

score 229 · Answer 6 · 2020-01-22 07:23:32

229

Views

Find Polynomial With roots that are the square of the original roots.

Published on 22 Jan 2020 - 7:23

score 557 · Answer 7 · 2020-02-01 22:30:40

557

Views

Sum of two perfect squares is also a perfect square. Proof that one of these numbers is divisible by 3

Published on 01 Feb 2020 - 22:30

score 155 · Answer 8 · 2020-02-10 03:12:14

155

Views

Find the asymptotic expansion as $N \rightarrow \infty$ of $\sum_{n=1}^{n_{\max}} \left\lceil{\sqrt{2nN+n^2}}\right\rceil$

Published on 10 Feb 2020 - 3:12

score 1.3k · Answer 9 · 2020-02-10 14:32:41

1.3k

Views

Sum of squares compared to square of sum, divided by number of elements being summed

Published on 10 Feb 2020 - 14:32

score 278 · Answer 10 · 2020-02-10 15:41:27

278

Views

$-1$ is not a sum of two squares in $\mathbb{Q}(\sqrt{-7})$

Published on 10 Feb 2020 - 15:41

score 95 · Answer 11 · 2020-02-14 09:17:40

95

Views

How can we prove that we have $2^{k-1}$ distinct representations as a sum of two squares?

Published on 14 Feb 2020 - 9:17

score 96 · Answer 12 · 2020-02-14 12:10:48

96

Views

Number of primitive representations?

Published on 14 Feb 2020 - 12:10

score 162 · Answer 13 · 2020-02-25 19:34:27

162

Views

Calculate exactly and as $N \rightarrow \infty$ of $\sum_{k=1}^{\left\lfloor{N/2}\right\rfloor} \left[{\sqrt{{N}^{2}+{k}^{2}} \in \mathbb{Z}}\right]$

Published on 25 Feb 2020 - 19:34

score 33 · Answer 14 · 2020-02-27 13:39:47

33

Views

Does Bachet's conjecture hold if the numbers that are squared are required to be unique?

Published on 27 Feb 2020 - 13:39

score 114 · Answer 15 · 2020-02-29 15:43:10

114

Views

Can a sum arithmetic square ever equal to power of two?

Published on 29 Feb 2020 - 15:43

List Question

Solving $x^2 + y^2 = M$ over integers

Solving $x^2 + y^2 = M$ with $M$ prime

Knowing $2017 = 9^2 + 44^2$. find $m,n$ which satisfy $2017^2 = m^2 + n^2$

Find the asymptotic expansion as $N \rightarrow \infty$ of $\sum_{k=1}^{\left\lfloor{N/2}\right\rfloor} \left\{{\sqrt{{N}^{2}+{k}^{2}}}\right\}$

Prove that $A^2=a_1^2+a_2^2-a_3^2-a_4^2$ for all integers $A$.

Find Polynomial With roots that are the square of the original roots.

Sum of two perfect squares is also a perfect square. Proof that one of these numbers is divisible by 3

Find the asymptotic expansion as $N \rightarrow \infty$ of $\sum_{n=1}^{n_{\max}} \left\lceil{\sqrt{2nN+n^2}}\right\rceil$

Sum of squares compared to square of sum, divided by number of elements being summed

$-1$ is not a sum of two squares in $\mathbb{Q}(\sqrt{-7})$

How can we prove that we have $2^{k-1}$ distinct representations as a sum of two squares?

Number of primitive representations?

Calculate exactly and as $N \rightarrow \infty$ of $\sum_{k=1}^{\left\lfloor{N/2}\right\rfloor} \left[{\sqrt{{N}^{2}+{k}^{2}} \in \mathbb{Z}}\right]$

Does Bachet's conjecture hold if the numbers that are squared are required to be unique?

Can a sum arithmetic square ever equal to power of two?

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