PTNN: 1+20x+22y+xy=0

`1+20x+22y+xy=0`

`<=>` `(y+20)x+22y+1=0`

`<=>` `x=-(22y+1)/(y+20)` `(y ne -20)`

`<=>` `x=-(22(y+20)-439)/(y+20)`

`<=>` `x=-22+439/(y+20)`

Mà `x in ZZ` và `y in ZZ`

`=>` `(y + 20) in Ư(439)={+-1;+-439}`

Ta có bảng sau:

\begin{array}{|c|c|c|}\hline \text{y+20}&\text{-439}&\text{-1}&\text{1}&\text{439}\\\hline \text{y}&\text{-459}&\text{-21}&\text{-19}&\text{419}\\\hline \text{x}&\text{-23}&\text{-461}&\text{417}&\text{-21}\\\hline\end{array}

Vậy phương trình có các nghiệm nguyên `S={(-23;-459);(-461;-21);(417;-19);(-21;419)}`

$\\$

`\bb\color{#3a34eb}{\text{@hoanganhnguyen09302}}`