We extend theorems of Serret and Pavone for solving f(x,y) = ax2 + bxy + cy2 = μ, where a 0, gcd(x, y) = 1, y 0. Here d = b2 - 4ac 0 is not a perfect square and $0 |μ| √d/2. If μ 0, Serret proved that x/y is a convergent to ρ = (-b + √d)/2a or σ = (-b - √d)/2a. If μ 0, we are able to modify Pavone's approach and show that with at most one exception, the solutions are convergents to ρ or σ.
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