Find the minimum in a proper subset with those condtions
Number Theory
Level
2
\(A\) is a non-empty proper subset of \(\mathbb Z\) with at least two elements, and with the following property:
If \(a\) and \(b\) are distinct elements of \(A,\) then \(-a,\) \(a+2b,\) and \(a+19\) are also elements of \(A.\)
Find \(\min \limits_{\substack{a \in A \\ a \neq 0}}\big(|a|\big).\)
by
Othman Slassi