According to Bézout's identity, the gcd(a,b) of two non-zero integers is equal to a linear combination of a and b, i.e. there exists integers x and y such that gcd(a,b)=xa+yb. My question is: does the converse also hold? i.e.: if for two non-zero integers a,b there exists integers x,y such that xa+yb=d, is then d=gcd(a,b)?

Thanks in advance.