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Home » Therefore, the largest possible value of \(\gcd(x, y)\) is \(oxed50\). - Londonproperty

Therefore, the largest possible value of \(\gcd(x, y)\) is \(oxed50\). - Londonproperty

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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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 \((x,y)\)?
Suppose \((m,n)\) and \((m',n')\) give same \((x,y)\): then \(m + n =...
From second: \(n = m + y\), substitute: \(m(m + y) = 506\), and \(m(n'...
Instead, note that \(x = m + n\), \(y = n - m\), so \(x^2 - y^2 = (m+n...
And different \((m,n)\) may give same \((x,y)\)?
Suppose \((m_1, n_1)\) and \((m_2, n_2)\) give same \((x,y)\):
Then \(m_1 + n_1 = m_2 + n_2\) and \(n_1 - m_1 = y\).

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