Tìm x, y thuộc ℤ biết 3xy - 2x + 5y = 29

3xy − 2x + 5y = 29

9xy − 6x + 15y = 87

(9xy − 6x) + (15y − 10) = 77

3x(3y − 2) + 5(3y−2) = 77

(3y − 2)(3x + 5) = 77

⇒ (3y − 2) và (3x + 5) là Ư(77) = {±1, ±7, ±11, ±77}

Ta có bảng giá trị sau:

3x + 5	–77	–11	–7	–1	1	7	11	77
3y – 2	–1	–7	–11	–77	77	11	7	1
x	\(\frac{{ - 82}}{3}\)	\(\frac{{ - 16}}{3}\)	–4	–2	\(\frac{{ - 4}}{3}\)	\(\frac{2}{3}\)	2	24
y	\(\frac{1}{3}\)	\(\frac{{ - 5}}{3}\)	–3	–25	\(\frac{{79}}{3}\)	\(\frac{{13}}{3}\)	3	1

Do x, y ∈ ℤ nên (x,y) ∈ {(−4; −3), (−2; −25), (2; 3), (24; 1)}

Vậy (x,y) ∈ {(−4; −3); (−2; −25); (2; 3); (24; 1)}.