Call x=X+1 and y=Y+1
Where x and y are positive integers
X,Y where non-negative implies X+1,Y+1 are positive.
Thus, you need to show for a,b not equal to zero,
The linear diophantine equation,
Has no positive solutions.
Begin by noting the trivial solutions:
(x,y)=(b,0) and (x,y)=(0,a)
Then use them to construct your basis of solutions.
But I did not get any further.