Prove that of a,b,c are natural numbers

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SUMMARY

The discussion focuses on proving that for natural numbers a, b, and c, if gcd(a, c) = 1 and b divides c, then gcd(a, b) must also equal 1. The proof requires a clear understanding of the definition of the greatest common divisor (gcd) and its properties, particularly regarding divisibility. Participants emphasize the importance of establishing the relationship between divisors of b and c to support the proof. The discussion highlights the necessity of using fundamental properties of gcd in number theory.

PREREQUISITES
  • Understanding of greatest common divisor (gcd) definitions and properties
  • Knowledge of natural numbers and their characteristics
  • Familiarity with divisibility concepts in number theory
  • Basic proof techniques in mathematics
NEXT STEPS
  • Study the properties of gcd, including the Euclidean algorithm
  • Explore the implications of divisibility in number theory
  • Learn about prime factorization and its relation to gcd
  • Investigate mathematical proof techniques, particularly in number theory
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Mathematics students, educators, and anyone interested in number theory or proof techniques in mathematics.

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I would greatly appreciate if someone just at least put me in the right direction with this. I have to prove this:

Prove that of a,b,c are natural numbers, gcd(a,c) = 1 and b divides c, then gcd(a,b) = 1.
 
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Write down the definition of gcd, what properties does gcd have, in particular gdc(x,y) and dividing x and y. Consider if d is a divisor of b then is it a divisor of c?
 

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