List questions from sums-of-squares

Published on 16 May 2015 - 14:19

108

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Show that there are infinitely many primes $p$ of the form $p=a^2+b^2+c^2+1$

Published on 16 May 2015 - 14:57

124

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Is it possible to have $a^2 + b^2 = c^2 + 1$ for $a$, $b$, $c$ being coprime integers?

Published on 29 May 2015 - 16:51

1.2k

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Can a number be equal to the sum of the squares of its prime divisors?

Published on 02 Jun 2015 - 16:04

540

Views

find all natural solution that satisfy $x^2+y^2 = 3z^2$

Published on 25 Mar 2026 - 6:10

543

Views

Find all natural solutions to $x^2+2y^2 = z^2$

Published on 09 Jun 2015 - 20:27

787

Views

Combining sums and/or differences of squares

Published on 24 Jun 2015 - 16:15

691

Views

How to derive the formula for the sum of the first $n$ perfect squares?

Published on 25 Jun 2015 - 19:18

169

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Infimum taken over $\lambda$ in $\mathbb{C}$

Published on 27 Jun 2015 - 4:09

131

Views

$5^m$, where m is any natural, can be expressed as the sum of two perfect squares?

Published on 02 Jul 2015 - 0:50

307

Views

trigonometric finite series equals to polynomial function

Published on 28 Mar 2026 - 10:26

94

Views

How to show that that the following three consecutive numbers $3^{2^{10}} − 1$, $3^{2^{10}}$,$3^{2^{10}}+ 1$ are the sum of two squares?

Published on 10 Jul 2015 - 13:36

891

Views

Express 2104 as the sum of four squares

Published on 10 Jul 2015 - 14:31

155

Views

Square matrix whose sum of squared elements equals 1.

Published on 22 Jul 2015 - 20:28

92

Views

On Catalan's complete solution to the equation $T^2=U^2+V^2+W^2$

Published on 24 Jul 2015 - 22:23

List Question

Is it known whether any positive integer can be written as the sum of $n$ different squares?

Show that there are infinitely many primes $p$ of the form $p=a^2+b^2+c^2+1$

Is it possible to have $a^2 + b^2 = c^2 + 1$ for $a$, $b$, $c$ being coprime integers?

Can a number be equal to the sum of the squares of its prime divisors?

find all natural solution that satisfy $x^2+y^2 = 3z^2$

Find all natural solutions to $x^2+2y^2 = z^2$

Combining sums and/or differences of squares

How to derive the formula for the sum of the first $n$ perfect squares?

Infimum taken over $\lambda$ in $\mathbb{C}$

$5^m$, where m is any natural, can be expressed as the sum of two perfect squares?

trigonometric finite series equals to polynomial function

How to show that that the following three consecutive numbers $3^{2^{10}} − 1$, $3^{2^{10}}$,$3^{2^{10}}+ 1$ are the sum of two squares?

Express 2104 as the sum of four squares

Square matrix whose sum of squared elements equals 1.

On Catalan's complete solution to the equation $T^2=U^2+V^2+W^2$

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