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Home » Thus, the probability is $ \frac144256 = \frac916 $. - Parker Core Knowledge

Thus, the probability is $ \frac144256 = \frac916 $. - Parker Core Knowledge

📅 May 5, 2026 👤 scraface

May 05, 2026

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= 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 \(4mn = 2024 \Rightarrow mn = 506\).
Now \(506 = 2 \cdot 11 \cdot 23\), so it has \((1+1)(1+1)(1+1) = 8\) p...
Thus, 16 valid pairs \((m, n)\), each giving a unique \((x, y)\):
x = \frac{2m + 2n}{2} = m + n, \quad y = \frac{2n - 2m}{2} = n - m
Each such pair yields an integer solution. Therefore, there are 16 lat...
But note: each solution \((x, y)\) is counted once for each factor pai...

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