/sci/ - Science & Math » Thread #14411604

2KiB, 400x200, problem.png

View Same Google iqdb SauceNAO

Problem for /sci/ to solve

Anonymous Wed 20 Apr 02:19:43 2022 No.14411604 View Reply Original Report

Quoted By: >>14411613 >>14412579 >>14412901 >>14414574 >>14415403

Does picrel have a positive integer solution for every 'n' when n > 1?

Anonymous

Anonymous Wed 20 Apr 2022 02:22:59 No.14411613 Report

Quoted By: >>14411662 >>14414574

>>14411604
no because you can't get one for n=5
https://www.youtube.com/watch?v=jeRsjAg3rNY

Anonymous

Anonymous Wed 20 Apr 2022 02:42:34 No.14411662 Report

Quoted By: >>14412884 >>14414574

>>14411613
n=5
x,y,z=2, 5, 10

Anonymous

Anonymous Wed 20 Apr 2022 10:51:31 No.14412491 Report

Quoted By: >>14414574

X=2
Y=2
Z=2

1/2=0.5
0.5x3=1.5

4/2.6666…=1.5
N=2.6666…

Anonymous

Anonymous Wed 20 Apr 2022 11:42:40 No.14412579 Report

Quoted By: >>14412907

>>14411604
X=Y=Z=3
N = 4

Anonymous

View Same Google iqdb SauceNAO Screenshot_20220420-165306_Scien (...).jpg, 449KiB, 1080x2177

Anonymous Wed 20 Apr 2022 13:54:09 No.14412884 Report

Quoted By:

>>14411662
Seems to be really close but not quite. Is n=5 really impossible?

Anonymous

Anonymous Wed 20 Apr 2022 14:02:02 No.14412901 Report

Quoted By: >>14413338

>>14411604
n = 4

x = 1
y = -1

z = 1

Anonymous

Anonymous Wed 20 Apr 2022 14:03:03 No.14412907 Report

Quoted By:

>>14412579
This one works

Anonymous

Anonymous Wed 20 Apr 2022 17:04:37 No.14413338 Report

Quoted By:

>>14412901
>positive integer solution

Anonymous

View Same Google iqdb SauceNAO FoxitReader_uFLoVO0feX.png, 66KiB, 978x289

Anonymous Wed 20 Apr 2022 18:51:47 No.14413637 Report

Quoted By: >>14413822 >>14414363 >>14416016

Spoiler alert

Anonymous

Anonymous Wed 20 Apr 2022 20:08:00 No.14413822 Report

Quoted By: >>14416016

>>14413637
Not sure what any of this gobbledygook is trying to say so here's the real answer:
>For any n>1, let x = floor(n/4 + 1)
>y = (n*x + n)/(4x - n)
>Rearrange the above formula to get:
>y(4x - n) = (nx + n) -> 4xy - ny = nx + n -> 4xy - nx - ny = n
>Let z = xy
>nz = (4xy - nx - ny)z -> (4xy - nx - ny)/nz = 1/z ->
>4xy/nxy - nx/nxy - ny/nxy = 1/z -> 4/n = 1/x + 1/y + 1/z

Anonymous

View Same Google iqdb SauceNAO 1646003263139.jpg, 9KiB, 466x91

Anonymous Thu 21 Apr 2022 00:49:34 No.14414363 Report

Quoted By:

>>14413637
cool but I would like to see how the author worked out pic rel.
Unfortunately you can't learn that stuff without practicing on your own.

Anonymous

Anonymous Thu 21 Apr 2022 02:50:56 No.14414574 Report

Quoted By:

>>14411613
>you can't get one for n=5
>>14411662

>>14411604
>positive integer solution
>>14412491
>N=2.6666…

the absolute state of this board

Anonymous

Anonymous Thu 21 Apr 2022 13:18:49 No.14415403 Report

Quoted By: >>14415747

>>14411604
$\begin{eqnarray*} \frac{4}{n} &=& \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \\ &=& \frac{1*a}{x*a = n} + \frac{1*b}{y*b = n} + \frac{1*c}{z*c = n} \\ &=& \frac{a}{n} + \frac{b}{n} + \frac{c}{n} \\ &=& \frac{a + b + c}{n} \\ &\Rightarrow& a + b + c = 4 \end{eqnarray*}$
therefore to find a or b or c, you gotta divide 4 by 3 in which you're forced to use fraction
so, no you can't have integer for x, y, z

Anonymous

Anonymous Thu 21 Apr 2022 15:48:08 No.14415747 Report

Quoted By: >>14417555 >>14417582

>>14415403
wrong, there exists an integer solution for all n>1, and even where z = x*y

Anonymous

Anonymous Thu 21 Apr 2022 17:31:21 No.14416016 Report

Quoted By: >>14416205 >>14416219

>>14413822
Doesn't guarantee integer solutions, no idea why you thought it did.
>let n = 13
>x = 4
>y = (13*4+13)/3 = 65/3

>>14413637
This only proves that integers with a prime factor equal to 3 mod 4 (which is almost all) can be written as such, it doesn't work for all n>1.
If we can prove that it holds for n whose prime factors are all equal to 1 mod 4, then the statement holds generally.

Anonymous

Anonymous Thu 21 Apr 2022 18:54:18 No.14416205 Report

Quoted By: >>14416219

>>14416016
>Doesn't guarantee integer solutions, no idea why you thought it did.
Oh shit you're right

Anonymous

Anonymous Thu 21 Apr 2022 18:57:48 No.14416216 Report

Quoted By:

https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Straus_conjecture

Anonymous

Anonymous Thu 21 Apr 2022 18:59:14 No.14416219 Report

Quoted By:

>>14416016
>>14416205
I'm going to rework what I did, the first term is still floor(n/4 + 1) though.

Anonymous

Anonymous Fri 22 Apr 2022 05:23:01 No.14417555 Report

Quoted By: >>14418429

>>14415747
show me the value of x,y and z then

Anonymous

Anonymous Fri 22 Apr 2022 05:39:39 No.14417582 Report

Quoted By: >>14418429

>>14415747
like this?
$\begin{eqnarray*} \frac{4}{n} &=& \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \\ &=& \frac{1}{2} + \frac{1}{3} + \frac{1}{6} \\ \frac{6}{6} &=& \frac{3}{6} + \frac{2}{6} + \frac{1}{6} \\ \frac{4}{6} &=& \frac{6}{6} \end{eqnarray*} $

Anonymous

Anonymous Fri 22 Apr 2022 12:50:08 No.14418083 Report

Quoted By: >>14418084

By the Erdos-Straus (I think) theorem, that equation has non-trivial solutions for every natural n

Anonymous

Anonymous Fri 22 Apr 2022 12:51:33 No.14418084 Report

Quoted By:

>>14418083
FUCK I looked it up and it's a conjecture not a theorem FUCK NIGGERS

Anonymous

Anonymous Fri 22 Apr 2022 16:00:45 No.14418429 Report

Quoted By:

>>14417555
>>14417582
I now realize this problem is beyond my means.

Anonymous

Anonymous Sat 23 Apr 2022 05:05:21 No.14420148 Report

Quoted By:

i can only think of niggers when i see the letter n

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches