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Home » Substitute \(a = 2\) into the equation \(a(a+b) = 2a + 3b\): - Dyverse

Substitute \(a = 2\) into the equation \(a(a+b) = 2a + 3b\): - Dyverse

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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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...
Another: \(m = -1\), \(n = -506\): \(x = -507/2\), not integer — wait!...
But when we list all divisor pairs \((m,n)\) with \(mn = 506\), we inc...
No: for each factorization, we get a point. But since \(m\) and \(n\)...
But each pair \((m,n)\) with \(mn = 506\) gives a unique \((x,y)\)?

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