- #1
Ratpigeon
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Homework Statement
define the gcd of a set of n integers, S={a_1...a_n}
Prove that exists and can be written as
q_1 a_1+...+q_n a_n for some integers, q_1...q_n
Homework Equations
Euclid's Algorithm?
The Attempt at a Solution
I have the statement that gcd(a_1...a_n) = min( gcd(a_i, a_j) i,j[itex]\in[/itex]{1...n})
and then I know that I can say since any two numbers have a gcd, the gcd exists, and can be represented as a linear combination of the a_i and a_j that have the minimal gcd, but I don't know how to prove the first statement.