Question

Arithmetic Derivative on sum of two perfect squares

score 40 · Answer 1 · 2019-04-19 18:13:08

40

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Arithmetic Derivative on sum of two perfect squares

Published on 19 Apr 2019 - 18:13

score 1.8k · Answer 2 · 2019-04-25 17:58:22

1.8k

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Finding an equivalence classes for the relation $(x_1,y_1)\sim(x_2,y_2)\ \iff\ x_1^2+y_1^2=x_2^2+y_2^2$.

Published on 25 Apr 2019 - 17:58

score 775 · Answer 3 · 2019-04-26 08:59:41

775

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If $ a, b, c$ are real numbers such that $a^2 + b^2 + c^2 = 1$, then show $ab+bc+ca> \frac{-1}{2}$

Published on 26 Apr 2019 - 8:59

score 389 · Answer 4 · 2026-03-25 23:22:53

389

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Prove that if $m^2+n^2=0$ then $m=0$ and $n=0$

Published on 25 Mar 2026 - 23:22

score 164 · Answer 5 · 2026-03-25 11:17:37

164

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Pattern in Squared Numbers and their Digit Sum

Published on 25 Mar 2026 - 11:17

score 122 · Answer 6 · 2019-06-22 00:45:03

122

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The sum of an infinite series containing a finite series in each denominator

Published on 22 Jun 2019 - 0:45

score 51 · Answer 7 · 2019-06-23 07:18:17

51

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How often can a number be written as a linear combination of the squares of its prime divisors?

Published on 23 Jun 2019 - 7:18

score 63 · Answer 8 · 2026-03-25 22:03:26

63

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Sum of harmonic numbers $H_{n+k}$

Published on 25 Mar 2026 - 22:03

score 388 · Answer 9 · 2026-03-26 04:32:18

388

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Solutions to a system of three equations with Pythagorean triples

Published on 26 Mar 2026 - 4:32

score 75 · Answer 10 · 2019-07-01 15:13:15

75

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Prove that $x^2+2y^2+3z^2=10a^2$ has no integer solutions aside from all of them being 0

Published on 01 Jul 2019 - 15:13

score 808 · Answer 11 · 2026-03-26 04:51:04

808

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Any positive integer can be written as sum / difference of consecutive squares

Published on 26 Mar 2026 - 4:51

score 132 · Answer 12 · 2019-08-06 10:39:56

132

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Primes of the form $a^2+b^2+c^2$, $0<a<b<c$

Published on 06 Aug 2019 - 10:39

score 436 · Answer 13 · 2019-08-09 16:12:18

Let a and b be natural numbers such that $2a - b, a - 2b$ and $a + b$ are all distinct squares. What is the smallest possible value of $b$?

score 59 · Answer 14 · 2019-09-02 15:12:33

59

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How to show the following result in number theory?

Published on 02 Sep 2019 - 15:12

score 292 · Answer 15 · 2026-03-26 06:22:19

292

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Conjecture: Any sufficiently big sum of three squares can be written as a square sum of three different natural numbers greater than zero

Published on 26 Mar 2026 - 6:22

List Question

Arithmetic Derivative on sum of two perfect squares

Finding an equivalence classes for the relation $(x_1,y_1)\sim(x_2,y_2)\ \iff\ x_1^2+y_1^2=x_2^2+y_2^2$.

If $ a, b, c$ are real numbers such that $a^2 + b^2 + c^2 = 1$, then show $ab+bc+ca> \frac{-1}{2}$

Prove that if $m^2+n^2=0$ then $m=0$ and $n=0$

Pattern in Squared Numbers and their Digit Sum

The sum of an infinite series containing a finite series in each denominator

How often can a number be written as a linear combination of the squares of its prime divisors?

Sum of harmonic numbers $H_{n+k}$

Solutions to a system of three equations with Pythagorean triples

Prove that $x^2+2y^2+3z^2=10a^2$ has no integer solutions aside from all of them being 0

Any positive integer can be written as sum / difference of consecutive squares

Primes of the form $a^2+b^2+c^2$, $0<a<b<c$

Let a and b be natural numbers such that $2a - b, a - 2b$ and $a + b$ are all distinct squares. What is the smallest possible value of $b$?

How to show the following result in number theory?

Conjecture: Any sufficiently big sum of three squares can be written as a square sum of three different natural numbers greater than zero

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