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📝 Recent Posts

We seek integer solutions \((x, y)\) to the equation \(x^2 - y^2 = 202...
This factors as:
Let \(a = x - y\) and \(b = x + y\), so \(ab = 2024\), and \(x = \frac...
For \(x\) and \(y\) to be integers, \(a + b\) and \(b - a\) must both...
Now factor 2024:
= 2^3 \cdot 11 \cdot 23
The total number of positive divisors is \((3+1)(1+1)(1+1) = 16\). So...
But only pairs where \(a\) and \(b\) have the same sign and same parit...
For \(x\) and \(y\) to be integers, \(a\) and \(b\) must both be even...
Let \(a = 2m\), \(b = 2n\), then \(4mn = 2024 \Rightarrow mn = 506\).

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