For which a,b,c is the diophantine quadratic equation

London Douglas

London Douglas

Answered question

2022-03-24

For which a,b,c is the diophantine quadratic equation ax2+bx+c=y2 souble?

Answer & Explanation

Karsyn Wu

Karsyn Wu

Beginner2022-03-25Added 17 answers

Step 1
Solve for x to get
x=b±b24ac+4ay22a
so you need b24ac+4ay2 to be a square, lets say b24ac+4ay2=z2
If a is negative it's easy to see that you need only a finite search. That's also the case if a is a square.
The remaining cases are studied under the name of generalized Pell's equation

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