Solution
= Solution
The convergents begin
$$
2, 3, \frac52, \frac83, \frac{37}{14},\ldots.
$$
Since
$$
8^2-7\cdot3^2=1,
$$
a strictly positive solution is $(x,y)=(8,3)$.
= Solution
The convergents begin
$$
2, 3, \frac52, \frac83, \frac{37}{14},\ldots.
$$
Since
$$
8^2-7\cdot3^2=1,
$$
a strictly positive solution is $(x,y)=(8,3)$.