True or False: a) If (a,b)=d and s*a+t*b=d then (s,t)=1 b) If (a, b) = d, then the equation a x + b y = d has one and only one solution x, y

Question

Any explanation on how to solve this would be greatly appreciated. Thank you.

True or False? Justify your answer.

Let a and b be two natural numbers.

(A) If (a,b)=d and sa+tb=d then (s,t)=1

(B) If (a, b) = d, then the equation a x + b y = d has one and only one solution x, y

for b)i know that it relates to this proposition: Let x0,y0 be a solution of ax + by = c. Then the general solution of ax+by = c is of the form x = x0 +z,y = y0 +w, where z,w is any solution of ax+by=0.