Elementary Methods in Number Theory Exercise 1.2.4

Construct four relatively prime integers $a,b,c,d$ such that no three of them are relatively prime.

Solve:Let $a,b,c$ share a prime factor $3$.$a,b,d$ share a prime factor 2，$a,c,d$ share a prime factor $5$,$b,c,d$ share a prime factor $7$.Let

\begin{equation}
a=3\times 2\times 5=30
\end{equation}
\begin{equation}
b=3\times 2\times 7=42
\end{equation}
\begin{equation}
c=3\times 5\times 7=105
\end{equation}
\begin{equation}
d=2\times 5\times 7=70
\end{equation}
Done.