x-5xy-4y=3
=>x(1-5y)-4y+0,8=3,8
=>-x(5y-1)-0,8(5y-1)=3,8
=>(5y-1)(-x-0,8)=3,8
=>(5y-1)(-5x-4)=19
=>(5x+4)(5y-1)=-19
=>(5x+4;5y-1)∈{(1;-19);(-19;1);(-1;19);(19;-1)}
=>(5x;5y)∈{(-3;-18);(-23;2);(-5;20);(15;0)}
=>(x;y)∈{\(\left(-\frac35;-\frac{18}{5}\right);\left(-\frac{23}{5};\frac25\right);\left(-1;4\right);\left(3;0\right)\) }
mà x,y nguyên
nên (x;y)∈{(-1;4); (3;0)}