MHB Question about problem involving gcd

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The discussion revolves around understanding why \( d|\gcd(a,-b) \) holds true when \( d=\gcd(a,b) \). It is clarified that this relationship stems from the properties of the greatest common divisor (gcd). The participants emphasize that the gcd is unaffected by the sign of the second argument, thus confirming the statement. The initial confusion is resolved by recognizing this fundamental property of gcd. Overall, the discussion highlights the importance of understanding gcd properties in problem-solving.
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HelloI am studying the problem given in the attachement. In the solution given, it says "Similarly \( d|\gcd(a,-b) \) ". I could not understand why this is so.thanks
 

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IssacNewton said:
HelloI am studying the problem given in the attachement. In the solution given, it says "Similarly \( d|\gcd(a,-b) \) ". I could not understand why this is so.thanks
$d|\gcd(a,-b)$ follows from the fact that $d=\gcd(a,b)$.
 
thanks...I should have realized that...
 
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