Ta có

5(13x+18y)−4(7x+4y)5(13x+18y)−4(7x+4y)

=65x+90y−28x−16y=65x+90y−28x−16y

=37x+74y=37x+74y

=37(x+2y)=37(x+2y)

Ta có

Vì 7x+4y⋮377x+4y⋮37

⇔4(7x+4y)⋮37⇔4(7x+4y)⋮37

⇔5(13x+18y)⋮37⇔5(13x+18y)⋮37

Mà ( 5 ; 37 ) =1

=> 13x +18 y chia hết cho 37 (đpcm )