mersenneforum.org > Math Let y^2=xz-x^2+1, and if value of x is known, can y and z be directly calculated? Given all variable
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 2018-03-02, 03:31 #1 MARTHA   Jan 2018 43 Posts Let y^2=xz-x^2+1, and if value of x is known, can y and z be directly calculated? Given all variable Let y^2=xz-x^2+1, and if value of x is known, can y and z be directly calculated? Given all variables are Integers.
2018-03-02, 03:36   #2
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts

Quote:
 Originally Posted by MARTHA Let y^2=xz-x^2+1, and if value of x is known, can y and z be directly calculated? Given all variables are Integers.
Is this homework ?

2018-03-02, 05:12   #3
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

24·613 Posts

Quote:
 Originally Posted by MARTHA Let y^2=xz-x^2+1, and if value of x is known, can y and z be directly calculated? Given all variables are Integers.
Yes. There are an infinite amount of them. You can write your expression like
xz=y^2+x^2-1, or (divide both left and right by x) $$z=\frac{y^2+x^2-1}x$$, or $$z=\frac{y^2-1}x+x$$. Now you see that the only condition to have z integer is that y^2-1 is divisible by x. Pick any x, say x=5, then all y ending in 1, 4, 6, or 9 will have squares ending in 1 or 6, so y^2-1 will end in 0 or 5.

 2018-03-02, 05:21 #4 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2·1,087 Posts Wolfram Alpha link: https://www.wolframalpha.com/input/?...%2B+1+for+y,+z
 2018-03-02, 05:35 #5 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 24·613 Posts whaaa, haha
2018-03-02, 05:53   #6
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

2×1,087 Posts

Quote:
 Originally Posted by LaurV whaaa, haha Attachment 17790
It's not what it seems. It's not a case of Pet-Discrimination.
Dog-Health is more Number-Theory related.

 2018-03-02, 06:31 #7 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 980810 Posts I am innocent I just followed your link. However, for the top of my head I can not imagine what kind of association wolfram alfa did (I never searched for cats and dogs on my computers, either)
 2018-03-02, 06:40 #8 S485122     "Jacob" Sep 2006 Brussels, Belgium 22×439 Posts There is not enough data to DIRECTLY calculate y and z when x is known, even given the fact that all are integers, because there is not a unique solution. Jacob Last fiddled with by S485122 on 2018-03-02 at 06:47 Reason: removed the part doing the homework
 2018-03-02, 07:00 #9 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2·1,087 Posts Forgot to put the integer constraint. Solution doesn't really change but for whatever reason the engine also prints the "Implicit derivatives" Whatever that is. https://www.wolframalpha.com/input/?...r+the+integers
 2018-03-02, 09:59 #10 Thomas11     Feb 2003 191510 Posts Following LaurV's suggestion the following solution will be found: $$y = k\cdot x + 1$$ $$z = 2k + (k^2+1)\cdot x$$ for all $$k\in N$$
 2018-03-02, 12:37 #11 MARTHA   Jan 2018 538 Posts Thanks Thank you all !!! you guys are amazing

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