Prove that if gcd (a,b) = c, then bx congruences c (mod a) for some integer x.
Proof.
we have cx=a, cw=b, and ai+bj=c. I need a|bx-c for some x.
bx-c = cwx-c = aw-c = aw - ai - bj
now, how do I get an a out of the bj?
Prove that if gcd (a,b) = c, then bx congruences c (mod a) for some integer x.
Proof.
we have cx=a, cw=b, and ai+bj=c. I need a|bx-c for some x.
bx-c = cwx-c = aw-c = aw - ai - bj
now, how do I get an a out of the bj?