Question

$m$ and $n$ are odd numbers such that $|m^2 - n^2 + 1| \mid (n^2 - 1)$. Prove that $|m^2 - n^2 + 1|$ is a square number.

score 54 · Answer 1 · 2026-03-28 11:54:15

54

Views

$m$ and $n$ are odd numbers such that $|m^2 - n^2 + 1| \mid (n^2 - 1)$. Prove that $|m^2 - n^2 + 1|$ is a square number.

Published on 28 Mar 2026 - 11:54

score 132 · Answer 2 · 2026-03-28 04:00:52

132

Views

Optimal division on $\mathbb{Z} $

Published on 28 Mar 2026 - 4:00

score 148 · Answer 3 · 2019-09-04 08:17:47

148

Views

Division of prime numbers

Published on 04 Sep 2019 - 8:17

score 76 · Answer 4 · 2026-03-27 16:16:01

76

Views

Divisibility proof with coprimes of 6

Published on 27 Mar 2026 - 16:16

score 28 · Answer 5 · 2026-03-27 16:12:29

28

Views

Divisors of every integer in a set

Published on 27 Mar 2026 - 16:12

score 76 · Answer 6 · 2019-09-07 19:46:44

76

Views

Divisibility of $(x+2y)^{2n}-x^{2n}$ by $2$

Published on 07 Sep 2019 - 19:46

score 71 · Answer 7 · 2019-09-08 03:57:51

71

Views

Divisiblity proof with coprimes of 6

Published on 08 Sep 2019 - 3:57

score 43 · Answer 8 · 2026-03-27 08:46:41

43

Views

Number of arrangements of one $1$, two $2$'s, three $3$'s, four $4$'s, ..., and nine $9$'s (given constraints)

Published on 27 Mar 2026 - 8:46

score 69 · Answer 9 · 2019-09-09 10:05:35

69

Views

Prove that the expression is multiple of $35$

Published on 09 Sep 2019 - 10:05

score 271 · Answer 10 · 2019-09-10 09:32:59

271

Views

What are the possible integer values for $x,y,z$ if $792|\overline{5x36y98z2}$?

Published on 10 Sep 2019 - 9:32

score 36 · Answer 11 · 2019-09-11 09:10:16

36

Views

What are the possible values of the integers $x, y , z$?

Published on 11 Sep 2019 - 9:10

score 1.2k · Answer 12 · 2019-09-12 02:06:26

1.2k

Views

A mythical question about the fine-structure constant inverse approximation, $137$, and the telephone number for information, $411$.

Published on 12 Sep 2019 - 2:06

score 209 · Answer 13 · 2019-09-12 03:41:11

209

Views

Divisibility result by induction: $64 \mid 3^{2n + 2} - 8n - 9$

Published on 12 Sep 2019 - 3:41

score 1.8k · Answer 14 · 2019-09-12 15:19:11

1.8k

Views

Show that if $x^d -1$ divides $x^n -1$ if and only if $d$ divides $n$

Published on 12 Sep 2019 - 15:19

score 57 · Answer 15 · 2019-09-13 14:33:29

57

Views

In which rings $R$ does $a\mid xy$ imply the existence of $b\mid x$ and $c\mid y$ with $a=bc$?

Published on 13 Sep 2019 - 14:33

List Question

$m$ and $n$ are odd numbers such that $|m^2 - n^2 + 1| \mid (n^2 - 1)$. Prove that $|m^2 - n^2 + 1|$ is a square number.

Optimal division on $\mathbb{Z} $

Division of prime numbers

Divisibility proof with coprimes of 6

Divisors of every integer in a set

Divisibility of $(x+2y)^{2n}-x^{2n}$ by $2$

Divisiblity proof with coprimes of 6

Number of arrangements of one $1$, two $2$'s, three $3$'s, four $4$'s, ..., and nine $9$'s (given constraints)

Prove that the expression is multiple of $35$

What are the possible integer values for $x,y,z$ if $792|\overline{5x36y98z2}$?

What are the possible values of the integers $x, y , z$?

A mythical question about the fine-structure constant inverse approximation, $137$, and the telephone number for information, $411$.

Divisibility result by induction: $64 \mid 3^{2n + 2} - 8n - 9$

Show that if $x^d -1$ divides $x^n -1$ if and only if $d$ divides $n$

In which rings $R$ does $a\mid xy$ imply the existence of $b\mid x$ and $c\mid y$ with $a=bc$?

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