- #1
choob
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Homework Statement
find all orderde pairs of integers (x,y) such that x^2+y^2=4x+2y
Homework Equations
The Attempt at a Solution
rearrange to--> x^2=4x+2y-y^2
because x and y can only be integers, y(2-y) must be divisible by x
so y(2-y)>=x
y(2-y)=x(x-4)
x(x-4)>=x
x-4>=1
x>=5
however, if i test with the ordered pair (3, 3) the diophantine equation is true
x^2+y^2=4x+2y
9+9=12+6
18=18
help me please! thanks