Question 4
A set S of positive integers is called canalero if for any three distinct $a,b,c\in S$, a divides bc, b divides ca, and c divides ab.
a. Prove that for every finite set of positive integers $\{c_1,\ldots,c_n\}$ there are infinitely many positive integers k such that $\{kc_1,\ldots,kc_n\}$ is canalero.
b. Prove that for every integer $n\ge3$ there is a canalero set with exactly n elements, no integer greater than 1 dividing all its elements.
a. Prove that for every finite set of positive integers $\{c_1,\ldots,c_n\}$ there are infinitely many positive integers k such that $\{kc_1,\ldots,kc_n\}$ is canalero.
b. Prove that for every integer $n\ge3$ there is a canalero set with exactly n elements, no integer greater than 1 dividing all its elements.