Pell equation
Trivia · proposed by @vipproaccout
Which of the following is a true property of the Pell equation \(
X^2 - kY^2 = 1,
\) where $k$ is a positive integer that is not a perfect square, and $X, Y$ range over positive integers?
AFor every non-square positive integer $k$, the equation has infinitely many integer solutions $(X, Y)$.
BFor every positive integer value of $Y$, there exists an integer $X$ such that $(X, Y)$ is a solution.
CThere exists a non-square positive integer $k$ for which the equation has no integer solutions.
DFor every solution $(X, Y)$ with $X, Y$ positive, the sum $X + Y$ is never a perfect square.