London Douglas

2022-03-24

For which a,b,c is the diophantine quadratic equation $a{x}^{2}+bx+c={y}^{2}$ souble?

Karsyn Wu

Beginner2022-03-25Added 17 answers

Step 1

Solve for x to get

$x=\frac{-b\pm \sqrt{{b}^{2}-4ac+4a{y}^{2}}}{2a}$

so you need$b}^{2}-4ac+4a{y}^{2$ to be a square, lets say $b}^{2}-4ac+4a{y}^{2}={z}^{2$

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

Solve for x to get

so you need

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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