Discrete Math: Greatest Common Divisor

Question

I have a question I can not figure out (It's #2 in section 4.4 of the book Discrete and Combinatorial Mathematics, by Ralph P. Grimaldi).

$\mathbb{Z}^+$ = The set of all positive integers

$\mathbb{Z}$ = The set of all integers

For $a, b \in \mathbb{Z}^+$ and $s,t \in \mathbb{Z}$, what can we say about $\gcd(a,b)$ if:

$as + bt = 2$?

Answer 1

HINT: If $d\mid a$ and $d\mid b$, what else in the equation $as+bt=2$ must be divisible by $d$? You might also want to look up Bézout’s theorem.

Answer 2

Hint $\rm\:d\mid a,b\:\Rightarrow\:d\mid as+bt = 2$