Exercise 1.2.7 (Relatively prime and relatively prime by pairs)

Question

Exhibit three integers that are relatively prime but not relatively prime in pairs.

Richard Ganaye · Accepted Answer

\begin{proof} 
$6 = 2 	imes 3,10 = 2 	imes 5,15 = 3 	imes 5$ is such an example.

Then $$\mathrm{gcd}(6,10,15) = 1 $$ (see Exercise 1.2.3(e) : $-14 	imes 6 + 7 	imes 10 + 1 	imes 15 = 1$), but $$\mathrm{gcd}(6,10) = 2,\qquad \mathrm{gcd}(6,15) = 3,\qquad  \mathrm{gcd}(10,15) = 5.$$
\end{proof}

Exercise 1.2.7 (Relatively prime and relatively prime by pairs)

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Exercise 1.2.7 (Relatively prime and relatively prime by pairs)

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