Solve diophantine equation x 2 − 2 y 2 = x − 2 y

acsuvaic9

acsuvaic9

Answered

2022-07-17

Solve diophantine equation x 2 2 y 2 = x 2 y

Answer & Explanation

Selden1f

Selden1f

Expert

2022-07-18Added 14 answers

The equation is
x 2 x 2 ( y 2 y ) = 0 ( x 1 2 ) 2 2 ( y 1 2 ) 2 1 4 + 1 2 = 0
( x 1 2 ) 2 2 ( y 1 2 ) 2 = 1 4
Now substitute
x := x 1 2 , y := y 1 2
So that the equation becomes
x 2 2 y 2 = 1 4
and it now has the form you're used to.

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