May 3rd, 2014, 04:38 AM  #1 
Newbie Joined: May 2014 From: UK Posts: 4 Thanks: 0  Parabolas
Hello there, I've got the following problem that I require some help with: x^23y4=0, I need to find all values of (x,y) that are integers. Has anybody got any ideas? Ty in advance, Bearz 
May 3rd, 2014, 05:54 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra 
$$y = \frac{1}{3}(x  2)(x + 2)$$ Thus, given $x \in \mathbb{Z}$, $x  2 = 3k$ and $x+2 =3k$ ($k \in \mathbb{Z}$) give $y \in \mathbb{Z}$. So, all $x = 3k \pm 2$ are integer solutions which is the same as saying all integers not divisible by three. We can also investigate the $y$ values. $$y = k(3k \pm 4) = 3k^2 \pm 4k$$ Last edited by v8archie; May 3rd, 2014 at 06:05 AM. 

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