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Home » But absence of radius, perhaps assume unit radius? Not stated. - American Beagle Club

But absence of radius, perhaps assume unit radius? Not stated. - American Beagle Club

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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Since \(m, n\) range over all integer divisor pairs of 506, and \(x =...
For fixed \(mn = 506\), \(x = m+n\), \(y = n-m\) determined uniquely....
But since \(m\) runs over all 16 integer divisors of 506 (8 positive,...
However, consider symmetry: for example, \((m,n)\) and \((n,m)\) give:
So symmetric about x-axis. But both are distinct unless \(y = 0\).
But since 506 ≠ 0, no solution has \(y = 0\) (would require \(m = n\),...
But each \((m,n)\) is distinct, so 16 solutions.
But let’s test a small one: \(m = 1\), \(n = 506\):
\(a = 2\), \(b = 1012\), then \(x = (2+1012)/2 = 507\), \(y = (1012 -...
Check: \(507^2 - 505^2 = (507-505)(507+505) = 2 \cdot 1012 = 2024\), c...

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