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Home » 5c + d &= 110 \quad \text(Equation 2) - Nelissen Grade advocaten

5c + d &= 110 \quad \text(Equation 2) - Nelissen Grade advocaten

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Now \(506 = 2 \cdot 11 \cdot 23\), so it has \((1+1)(1+1)(1+1) = 8\) positive divisors, giving 8 positive and 8 negative pairs \((m, n)\).

📌 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 lattice points.

📌 But note: each solution \((x, y)\) is counted once for each factor pair. Since \( (a,b) \) and \( (b,a) \) yield potentially different \((x,y)\), but in our setup \(a = x - y\), \(b = x + y\), so order matters in assignment. However, fixing \(a, b\) as both even and same parity already covers all valid factorizations.

📌 Wait: we set \(ab = 2024\), and we require both \(a\) and \(b\) even.

📌 Total factor pairs (positive and negative) where both are even: Since 2024 is divisible by 4, and all factorizations into two evens are valid.

📌 But from the substitution, \(m n = 506\), and 506 is even, but not divisible by higher powers — all its factor pairs consist of one even and one odd? No:

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