+0  
 
0
33
2
avatar+41 

x^2 + y^2 = 2(x+y) + xy

what are all the possible solutions (x,y) if x and y are both integers?

hearts123  Nov 2, 2018
 #1
avatar+90968 
+1

x      y

0     0

2     0

0     2

2     4

4     2

4     4

 

 

cool cool cool

CPhill  Nov 3, 2018
 #2
avatar+90968 
+1

This may be a little difficult to solve algebraically  [ although there may be a way to do so ]

 

Look at the graph here :  https://www.desmos.com/calculator/oznsn0uwpe

 

Because of the presence of the xy term,  we have a rotated conic (ellipse??)  

 

We are looking for all the lattice points  (points with integer coordinates ) that this graph passes through

 

They are the  same ones I enumerated in my previous answer.......

 

 

cool cool cool

CPhill  Nov 3, 2018
edited by CPhill  Nov 3, 2018
edited by CPhill  Nov 3, 2018

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