Solution
= Solution
Take \b[$(a,b,c,n)=(1,4,2,6)$]. These are four distinct positive <integers> and $n\geq3$. Their products are $ac=2$ and $bc=8$, whose difference is $6$, so $ac\equiv bc\pmod6$. Here the correct reduced modulus is $6/\gcd(2,6)=3$, and indeed $1\equiv4\pmod3$. The example illustrates why cancelling a noninvertible factor may change the modulus in <modular arithmetic>.