I was solving the following linear diophantine equation :
$56x + 72y = 40 $ in integers.
My attempt: I got that 8 is the gcd of 56 and 72 and $8|40$ and hence a solution exists and I can write:
$8 = 56 - 16 *3 $
$\implies$ $ 8= 56 - (72 -56*1)*3$
$\implies$ $ 8= 4*56 - 3*72$.
So my answer is $x = 4$ and $y = -3$. But in book its showing $x = 20$ and $y = -15$. Where I went wrong? Kindly help.