Question about problem involving gcd

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SUMMARY

The discussion centers on the mathematical property that if \( d = \gcd(a, b) \), then it follows that \( d | \gcd(a, -b) \). This conclusion is derived from the fundamental definition of the greatest common divisor (gcd), which remains unchanged when one of the arguments is negated. Participants confirm this property as a standard result in number theory, emphasizing its importance in understanding gcd relationships.

PREREQUISITES

  • Understanding of the greatest common divisor (gcd)
  • Basic knowledge of number theory
  • Familiarity with mathematical notation and properties
  • Concept of divisibility in integers

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  • Study the properties of gcd in detail, including proofs and examples
  • Explore the Euclidean algorithm for calculating gcd
  • Learn about the implications of gcd in modular arithmetic
  • Investigate applications of gcd in solving Diophantine equations

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Students of mathematics, educators teaching number theory, and anyone interested in the properties of divisibility and gcd in integer arithmetic.

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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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