It's just Pell's equation
How many solutions does the equation
have in integers
and
?
Submit -1 as the answer if you think there are infinitely many integers.
Image Credit: Flickr Bswope .
The answer is 0.
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Note that, for the equation to hold, we must have x 2 ≡ − 1 m o d 1 2 . It is easy to confirm that − 1 is not a quadratic residual m o d 1 2 , so the equation has 0 solutions.