Question

Prove that for every positive integer $n$ there do not exist four positive integers $a,b,c,d$ with $ad = bc$ and $n^2 < a < b < c < d < (n+1)^2$.

score 139 · Answer 1 · 2026-04-15 04:39:58

139

Views

Prove that for every positive integer $n$ there do not exist four positive integers $a,b,c,d$ with $ad = bc$ and $n^2 < a < b < c < d < (n+1)^2$.

Published on 15 Apr 2026 - 4:39

score 133 · Answer 2 · 2026-04-10 07:14:17

133

Views

Finding integer roots of an equation

Published on 10 Apr 2026 - 7:14

score 238 · Answer 3 · 2026-04-15 13:26:49

238

Views

Find all integers $x$ so that there is an integer y so that ${x\choose y} = 1999000$.

Published on 15 Apr 2026 - 13:26

score 302 · Answer 4 · 2026-04-15 19:48:24

302

Views

find all positive integers that are the cube of the sum of their digits

Published on 15 Apr 2026 - 19:48

score 284 · Answer 5 · 2026-04-11 13:26:06

284

Views

find the smallest positive integer that can be written as a sum of two squares in three different ways

Published on 11 Apr 2026 - 13:26

score 70 · Answer 6 · 2026-04-16 00:37:26

70

Views

Integer solutions to $x^2 + (x-y)^2 = 17^2$, with $x\ge0$

Published on 16 Apr 2026 - 0:37

score 307 · Answer 7 · 2026-04-16 15:12:20

307

Views

Combinatorics with a set number of coins

Published on 16 Apr 2026 - 15:12

score 65 · Answer 8 · 2026-04-12 05:28:50

65

Views

Quadratic Diophantine equation

Published on 12 Apr 2026 - 5:28

score 60 · Answer 9 · 2026-04-14 01:05:46

60

Views

6th and 7th divisor of integer

Published on 14 Apr 2026 - 1:05

score 350 · Answer 10 · 2026-04-15 15:30:52

350

Views

What functions from $\Bbb N\to\Bbb N$ can be made from $+$, $-$, $\times$, $\div$, exponentiation, and $\lfloor\cdot\rfloor$?

Published on 15 Apr 2026 - 15:30

score 120 · Answer 11 · 2026-04-14 19:08:28

120

Views

Are there infinitely many $m$ such that $2^{2m+1}+17$ is a perfect square?

Published on 14 Apr 2026 - 19:08

score 94 · Answer 12 · 2026-04-16 08:20:27

94

Views

Solving $3 = x^2 + y^2 + z^2 - xy - yz - zx$ for integer $x$, $y$, $z$

Published on 16 Apr 2026 - 8:20

score 147 · Answer 13 · 2026-04-14 16:50:21

147

Views

How to solve the Diophantine equation: $x^3 + y^3 + xy = 223$ for all integer pairs $(x,y)$?

Published on 14 Apr 2026 - 16:50

score 120 · Answer 14 · 2026-04-13 18:53:54

120

Views

Diophantine Equations Problem

Published on 13 Apr 2026 - 18:53

score 98 · Answer 15 · 2026-04-15 20:12:32

98

Views

Find all positive integers x, y

Published on 15 Apr 2026 - 20:12

List Question

Prove that for every positive integer $n$ there do not exist four positive integers $a,b,c,d$ with $ad = bc$ and $n^2 < a < b < c < d < (n+1)^2$.

Finding integer roots of an equation

Find all integers $x$ so that there is an integer y so that ${x\choose y} = 1999000$.

find all positive integers that are the cube of the sum of their digits

find the smallest positive integer that can be written as a sum of two squares in three different ways

Integer solutions to $x^2 + (x-y)^2 = 17^2$, with $x\ge0$

Combinatorics with a set number of coins

Quadratic Diophantine equation

6th and 7th divisor of integer

What functions from $\Bbb N\to\Bbb N$ can be made from $+$, $-$, $\times$, $\div$, exponentiation, and $\lfloor\cdot\rfloor$?

Are there infinitely many $m$ such that $2^{2m+1}+17$ is a perfect square?

Solving $3 = x^2 + y^2 + z^2 - xy - yz - zx$ for integer $x$, $y$, $z$

How to solve the Diophantine equation: $x^3 + y^3 + xy = 223$ for all integer pairs $(x,y)$?

Diophantine Equations Problem

Find all positive integers x, y

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