Tìm x, y nguyên thỏa mãn x^2 + 5y^2 - 4xy - 4y
Giải thích
x2 + 5y2 – 4xy – 4y + 3 = 0
⇔ (x2 – 4xy + 4y2) + (y2 – 4y + 4) = 1
⇔ (x – 2y)2 + (y – 2)2 = 1
Vì x, y ∈ ℤ nên (x – 2y)2 + (y – 2)2 ≥ 0
Suy ra:
⇔ 
x2 + 5y2 – 4xy – 4y + 3 = 0
⇔ (x2 – 4xy + 4y2) + (y2 – 4y + 4) = 1
⇔ (x – 2y)2 + (y – 2)2 = 1
Vì x, y ∈ ℤ nên (x – 2y)2 + (y – 2)2 ≥ 0
Suy ra:
⇔