Question

Find all positive integers which are representable uniquely as $\frac{x^2+y}{xy+1}$ with $x,y$ positive integers.

score 203 · Answer 1 · 2026-04-02 07:07:32

203

Views

Find all positive integers which are representable uniquely as $\frac{x^2+y}{xy+1}$ with $x,y$ positive integers.

Published on 02 Apr 2026 - 7:07

score 146 · Answer 2 · 2020-06-02 16:24:31

146

Views

Positive integers $n$ with $n^5 - 5n^3 + 5n + 1 | n!$

Published on 02 Jun 2020 - 16:24

score 349 · Answer 3 · 2026-03-30 05:25:27

349

Views

If $3\mid mn$, then $3\mid m$ or $3\mid n$

Published on 30 Mar 2026 - 5:25

score 94 · Answer 4 · 2020-06-04 00:42:53

94

Views

given 9 consecutive naturals, no partition into two sets will give set one product = set two product

Published on 04 Jun 2020 - 0:42

score 120 · Answer 5 · 2020-06-04 19:30:55

120

Views

Is there a division-by-zero problem when we divide by pure imaginary numbers?

Published on 04 Jun 2020 - 19:30

score 61 · Answer 6 · 2020-06-07 12:15:10

61

Views

finding all numbers $a,b$ that divide $c$ but product of $a$ and $b$ does not divide $c$

Published on 07 Jun 2020 - 12:15

score 181 · Answer 7 · 2026-03-27 14:59:05

181

Views

How to use long division to compute the reciprocal $1/Q(s)$ of a generic polynomial?

Published on 27 Mar 2026 - 14:59

score 106 · Answer 8 · 2020-06-09 04:25:00

106

Views

How do I know that $3$ and $2 + \sqrt{-5}$ are not associates in $\mathbb Z[\sqrt{-5}]?$

Published on 09 Jun 2020 - 4:25

score 88 · Answer 9 · 2026-03-29 12:51:09

88

Views

When does $a\mid c$ and $b\mid c$ imply $ab\mid c$?

Published on 29 Mar 2026 - 12:51

score 825 · Answer 10 · 2026-03-30 05:31:55

825

Views

If $n$ is odd, then there is an integer $k$ such that $n^2=8k+1$

Published on 30 Mar 2026 - 5:31

score 130 · Answer 11 · 2026-03-30 13:04:00

130

Views

$2007^{201} + 2019^{201} - 1982^{201} - 2044^{201}$ is divisible by which of the following?

Published on 30 Mar 2026 - 13:04

score 83 · Answer 12 · 2020-06-10 17:03:02

83

Views

When the quotient $\frac {13n^2+n}{2n+2}$ is an integer?

Published on 10 Jun 2020 - 17:03

score 543 · Answer 13 · 2026-03-29 14:29:55

543

Views

Prove that if $gcd(a, b)=d$ then $gcd(a^2, b^2 )=d^2$

Published on 29 Mar 2026 - 14:29

score 727 · Answer 14 · 2026-02-23 10:18:23

727

Views

a and b both divide c and are coprime; does ab then also divide c?

Published on 23 Feb 2026 - 10:18

score 223 · Answer 15 · 2026-03-27 12:03:06

223

Views

Looking for divisibility by 29 and a general proof( if any)

Published on 27 Mar 2026 - 12:03

List Question

Find all positive integers which are representable uniquely as $\frac{x^2+y}{xy+1}$ with $x,y$ positive integers.

Positive integers $n$ with $n^5 - 5n^3 + 5n + 1 | n!$

If $3\mid mn$, then $3\mid m$ or $3\mid n$

given 9 consecutive naturals, no partition into two sets will give set one product = set two product

Is there a division-by-zero problem when we divide by pure imaginary numbers?

finding all numbers $a,b$ that divide $c$ but product of $a$ and $b$ does not divide $c$

How to use long division to compute the reciprocal $1/Q(s)$ of a generic polynomial?

How do I know that $3$ and $2 + \sqrt{-5}$ are not associates in $\mathbb Z[\sqrt{-5}]?$

When does $a\mid c$ and $b\mid c$ imply $ab\mid c$?

If $n$ is odd, then there is an integer $k$ such that $n^2=8k+1$

$2007^{201} + 2019^{201} - 1982^{201} - 2044^{201}$ is divisible by which of the following?

When the quotient $\frac {13n^2+n}{2n+2}$ is an integer?

Prove that if $gcd(a, b)=d$ then $gcd(a^2, b^2 )=d^2$

a and b both divide c and are coprime; does ab then also divide c?

Looking for divisibility by 29 and a general proof( if any)

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