Home / Let $a = x - y$ and $b = x + y$, so $ab = 2024$, and $x = \frac{a + b}{2}$, $y = \frac{b - a}{2}$.

Let $a = x - y$ and $b = x + y$, so $ab = 2024$, and $x = \frac{a + b}{2}$, $y = \frac{b - a}{2}$.

February 22, 2026

$Let $a = x - y$ and $b = x + y$, so $ab = 2024$, and $x = \frac{a + b}{2}$, $y = \frac{b - a}{2}$.$

Question:** How many lattice points lie on the hyperbola $x^2 - y^2 = 2024$ in the Cartesian plane?
We seek integer solutions $(x, y)$ to the equation $x^2 - y^2 = 2024$.
This factors as:
For $x$ and $y$ to be integers, $a + b$ and $b - a$ must both be even, so $a$ and $b$ must have the same parity.
Now factor 2024:
= 2^3 \cdot 11 \cdot 23