hi-dears-masters-A-au-bv-a-b-u-v-Z-4-with-a-b-1-prove-that-A-is-ideal-of-Z-2-let-Z-n-n-Z-prove-that-A-has-a-smaller-element-strictly-positive-such-that-A-Z

Question Number 147493 by henderson last updated on 21/Jul/21

hi, dears masters!

A = {a u + b v, (a, b, u, v) \in Z^{4}} with a \neq b .

1 . prove that A is ideal of Z .

2 . let λ Z = {λ n, n \in Z} .

prove that A has a smaller element λ strictly

positive such that A = λ Z .

3 . prove that λ = \gcd (a, b) .