Question

Conjecture: between any two consecutive squares, there are integers matching each of $2p, 3p,$ and $4p$; also, more terms with higher degrees

score 138 · Answer 1 · 2026-03-27 02:07:04

138

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Conjecture: between any two consecutive squares, there are integers matching each of $2p, 3p,$ and $4p$; also, more terms with higher degrees

Published on 27 Mar 2026 - 2:07

score 48 · Answer 2 · 2022-02-03 21:03:56

48

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How can we make this a perfect square?

Published on 03 Feb 2022 - 21:03

score 172 · Answer 3 · 2026-03-29 07:30:05

172

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How we may express four squares whose difference is each a square in terms of (preferably solid) geometry?

Published on 29 Mar 2026 - 7:30

score 247 · Answer 4 · 2026-02-24 05:32:15

247

Views

Perfect numbers and Pell's equation

Published on 24 Feb 2026 - 5:32

score 77 · Answer 5 · 2022-02-09 10:30:38

77

Views

Find the prime numbers $p, q$ satisfying perfect square

Published on 09 Feb 2022 - 10:30

score 361 · Answer 6 · 2022-02-11 14:20:59

361

Views

Find all integer pairs $(a,b)$ such that $a^2+ab+b^2=219^2$, without technology.

Published on 11 Feb 2022 - 14:20

score 215 · Answer 7 · 2022-02-17 08:05:19

215

Views

Let $w<x$ be integers with $x^2-w^2$ beeing a square. Which condition they must satisfy for a $y$ to exist with $y^2-x^2$, $y^2-w^2$ being squares?

Published on 17 Feb 2022 - 8:05

score 79 · Answer 8 · 2022-02-19 07:49:14

79

Views

find the $x$ of quadratic equation, such that the squre root of quadratic equation result is integer

Published on 19 Feb 2022 - 7:49

score 91 · Answer 9 · 2022-02-19 11:04:52

91

Views

Why do we have these occurrences of primes of the form $4k+1$ in square differences (Mengoli's Six-Square Problem)?

Published on 19 Feb 2022 - 11:04

score 325 · Answer 10 · 2026-03-27 21:19:03

325

Views

What are the remaining cases to consider for this problem, specifically all the possible premises for $i(q)$?

Published on 27 Mar 2026 - 21:19

score 83 · Answer 11 · 2026-04-02 16:19:28

83

Views

Can a perfect square N be composed by only 0 and 1? Where N's prime factor are only 3 and 7.

Published on 02 Apr 2026 - 16:19

score 66 · Answer 12 · 2022-02-26 10:36:11

66

Views

Let $w<x$ be integers with $x^2-w^2$ beeing a square. If no $y$ exists with $y^2-x^2$, $y^2-w^2$ being squares, can we show no $y$ exists for $nw<nx$?

Published on 26 Feb 2022 - 10:36

score 39 · Answer 13 · 2026-03-26 21:12:39

39

Views

Whole number solutions to $2n^4+1=m^2$.

Published on 26 Mar 2026 - 21:12

score 71 · Answer 14 · 2022-03-06 15:19:16

71

Views

Are there infinitely many square numbers with increasing digits?

Published on 06 Mar 2022 - 15:19

score 521 · Answer 15 · 2022-03-07 08:18:33

521

Views

Checking whether a number is a perfect square or not.

Published on 07 Mar 2022 - 8:18

List Question

Conjecture: between any two consecutive squares, there are integers matching each of $2p, 3p,$ and $4p$; also, more terms with higher degrees

How can we make this a perfect square?

How we may express four squares whose difference is each a square in terms of (preferably solid) geometry?

Perfect numbers and Pell's equation

Find the prime numbers $p, q$ satisfying perfect square

Find all integer pairs $(a,b)$ such that $a^2+ab+b^2=219^2$, without technology.

Let $w<x$ be integers with $x^2-w^2$ beeing a square. Which condition they must satisfy for a $y$ to exist with $y^2-x^2$, $y^2-w^2$ being squares?

find the $x$ of quadratic equation, such that the squre root of quadratic equation result is integer

Why do we have these occurrences of primes of the form $4k+1$ in square differences (Mengoli's Six-Square Problem)?

What are the remaining cases to consider for this problem, specifically all the possible premises for $i(q)$?

Can a perfect square N be composed by only 0 and 1? Where N's prime factor are only 3 and 7.

Let $w<x$ be integers with $x^2-w^2$ beeing a square. If no $y$ exists with $y^2-x^2$, $y^2-w^2$ being squares, can we show no $y$ exists for $nw<nx$?

Whole number solutions to $2n^4+1=m^2$.

Are there infinitely many square numbers with increasing digits?

Checking whether a number is a perfect square or not.

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