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Let a and b be integers, not both 0 and let d = gcd(a, b). Prove that if a = da and b =

Chapter 7, Problem 6

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QUESTION:

Let a and b be integers, not both 0 and let d = gcd(a, b). Prove that if a = da and b = db for some integers a and b, then gcd(a, b) = 1.

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QUESTION:

Let a and b be integers, not both 0 and let d = gcd(a, b). Prove that if a = da and b = db for some integers a and b, then gcd(a, b) = 1.

ANSWER:

Step 1 of 4

The Greatest Common Divisor (GCD) of non-zero integers  and is the best high-quality integer such that  is a divisor of each and; that is, there are integers and.

Such that and and d is the most important such integer.

The GCD of and is normally denoted

                                                                                         

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