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 𝛌Z = {𝛌n , n ∈ Z}. prove that A has a smaller element 𝛌 strictly positive such that A = 𝛌Z. 3. prove that 𝛌 = gcd(a,b).


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Question Number 147493 by henderson last updated on 21/Jul/21
$hi, dears masters ! A = {au+bv, (a, b, u, v) ∈ Z^4 } with a ≠ b. 1. prove that A is ideal of Z. 2. let 𝛌Z = {𝛌n , n ∈ Z}. prove that A has a smaller element 𝛌 strictly positive such that A = 𝛌Z. 3. prove that 𝛌 = gcd(a,b).$
$hi, dears masters!$ $A = {a u + b v, (a, b, u, v) \in Z^{4}} with a \neq b .$ $1 . prove that A is ideal of Z .$ $2 . let λ Z = {λ n, n \in Z} .$ $prove that A has a smaller element λ strictly$ $positive such that A = λ Z .$ $3 . prove that λ = \gcd (a, b) .$
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