Question

Hurwitz's matrix equations

score 211 · Answer 1 · 2016-03-14 16:31:00

211

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Hurwitz's matrix equations

Published on 14 Mar 2016 - 16:31

score 118 · Answer 2 · 2016-03-17 08:27:02

118

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Prove that for any prime $p$ there exist natural numbers $a,b$ for which $ p$ divides $a^2+b^2+1$

Published on 17 Mar 2016 - 8:27

score 222 · Answer 3 · 2016-03-17 13:35:25

222

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Write $x_n=22..244...45$ as sum of $2$ squares

Published on 17 Mar 2016 - 13:35

score 1.1k · Answer 4 · 2016-03-18 16:18:11

1.1k

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Sum of Consecutive Perfect Squares

Published on 18 Mar 2016 - 16:18

score 174 · Answer 5 · 2016-03-21 09:34:54

Let $n$ be a positive integer. Show that $n$ and $2n$ have the same number of representations as a sum of two squares of non-negative integers.

score 806 · Answer 6 · 2016-03-25 13:21:04

806

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Prove that there are arbitrarily long sequences of consecutive integers, none of which can be written as the sum of two perfect squares.

Published on 25 Mar 2016 - 13:21

score 1.9k · Answer 7 · 2016-03-28 17:45:39

1.9k

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What is the relation between the square root of the sum of squares and the sum of the absolute values?

Published on 28 Mar 2016 - 17:45

score 4.9k · Answer 8 · 2016-03-29 00:44:02

4.9k

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Why is the square root of a sum not equal to the square root of each its addends?

Published on 29 Mar 2016 - 0:44

score 5.1k · Answer 9 · 2016-03-30 21:04:01

5.1k

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Sums of squares minus square of sums

Published on 30 Mar 2016 - 21:04

score 138 · Answer 10 · 2026-03-28 07:57:10

138

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Relatively Prime Cases of the Brahmagupta-Fibonacci Identity

Published on 28 Mar 2026 - 7:57

score 1.4k · Answer 11 · 2016-04-06 11:33:26

1.4k

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If $n = a^2 + b^2 + c^2$ for positive integers $a$, $b$,$c$, show that there exist positive integers $x$, $y$, $z$ such that $n^2 = x^2 + y^2 + z^2$.

Published on 06 Apr 2016 - 11:33

score 1.4k · Answer 12 · 2016-04-07 14:33:48

1.4k

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Show that $x^2 + y^2 + z^2 = x^3 + y^3 + z^3$ has infinitely many integer solutions.

Published on 07 Apr 2016 - 14:33

score 450 · Answer 13 · 2016-04-08 09:47:40

450

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Upper bound for sum of squares given mean of elements

Published on 08 Apr 2016 - 9:47

score 1.8k · Answer 14 · 2016-04-09 16:25:35

1.8k

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Maximize sum of squares

Published on 09 Apr 2016 - 16:25

score 1.8k · Answer 15 · 2016-04-12 19:10:55

1.8k

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Triangular Numbers and Sum of Two Squares

Published on 12 Apr 2016 - 19:10

List Question

Hurwitz's matrix equations

Prove that for any prime $p$ there exist natural numbers $a,b$ for which $ p$ divides $a^2+b^2+1$

Write $x_n=22..244...45$ as sum of $2$ squares

Sum of Consecutive Perfect Squares

Let $n$ be a positive integer. Show that $n$ and $2n$ have the same number of representations as a sum of two squares of non-negative integers.

Prove that there are arbitrarily long sequences of consecutive integers, none of which can be written as the sum of two perfect squares.

What is the relation between the square root of the sum of squares and the sum of the absolute values?

Why is the square root of a sum not equal to the square root of each its addends?

Sums of squares minus square of sums

Relatively Prime Cases of the Brahmagupta-Fibonacci Identity

If $n = a^2 + b^2 + c^2$ for positive integers $a$, $b$,$c$, show that there exist positive integers $x$, $y$, $z$ such that $n^2 = x^2 + y^2 + z^2$.

Show that $x^2 + y^2 + z^2 = x^3 + y^3 + z^3$ has infinitely many integer solutions.

Upper bound for sum of squares given mean of elements

Maximize sum of squares

Triangular Numbers and Sum of Two Squares

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