then determine the value of gcd(a/d, b/d). Repeat Exercise (7a) with a = 10 and

Question

then determine the value of gcd(a/d, b/d). Repeat Exercise (7a) with a = 10 and b = 45. Let a, ,not both equal to 0. and let d = gcd(a,b). Explain why a/d and b/d are integers. Then prove that gcd(a/d,b/d)=1 Hint: Start by writing d as a linear combination of a and b. This says that if you divide both a and b by their greatest common divisor, the result will be two relatively prime integers. Are the following propositions C661true or false? Justify your conclusions. For all integers a, b, and c. if a|c and b | c, then (ab)| c. For all integers a, b, and c, if a | c, b | c and gcd(a, b)= 1, then (ab)| c.

Explanation / Answer

This is false. As a counterexample, let a = 2, b = 4 and c = 4. Then 2 | 4 and 4 | 4, but (ab) does not divide c because 8 does not divide 4.

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