Problem
NT-B1-M08-P016 Three Prescribed Divisors
#16
★★★☆☆ Level 3 of 5
Find all \(n\) such that \(5\mid n+1\), \(7\mid n+2\), \(11\mid n+3\).
In the example one solution was \(19\).
The system is equivalent to \(n\equiv4\pmod5\), \(n\equiv5\pmod7\), \(n\equiv8\pmod{11}\). One solution is \(n=19\). Since the moduli are pairwise coprime, all solutions are \(n\equiv19\pmod{385}\).
Distinguish “find one” from “find all”.