Let be integers, not both equal to zero, . Prove
Attempt: I can do final part of proof: If and , then . From , s.t. we have . From and finally .
But I can't prove that and .
Can anyone help please? Thank you!
Assume that a gives a remainder 0 < r < d when divided by d and prove that r is a linear combination of a and b smaller than d.
You need to make a restriction that some numbers are positive in this problem because d = min{ax + by | x, y in Z} does not exist.