`A=(4a+7b)(5a+4b) vdots 19`

Ta có `19` là số nguyên tố nên

`4a+7b vdots 19` hoặc `5a+4b vdots 19`

`TH1` `:4a+7b vdots 19`

`=>4a+7b+3(5a+4b)`

`=4a+7b+15a+12b`

`=19a+19b`

`=19(a+b) vdots 19`

Mà `4a+7b vdots 19`

`=>3(5a+4b) vdots 19`

`=>5a+4b vdots 19`

`=>A=(4a+7b)(5a+4b) vdots 19 xx 19 = 361`

`TH2` `5a+4b vdots 19`

`=>4a+7b+3(5a+4b)`

`=4a+7b+15a+12b`

`=19a+19b`

`=19(a+b) vdots 19`

Mà `5a+4b vdots 19`

`=>3(5a+4b) vdots 19`

`=>4a+7b vdots 19`

`=>A=(4a+7b)(5a+4b) vdots 19 xx 19 = 361`

Vậy `A vdots 361`