Problem
NT-B1-M08-P017 Shifts with \(3,5,7\)
#17
★★★☆☆ Level 3 of 5
Find the smallest positive \(n\) such that \(3\mid n+1\), \(5\mid n+2\), \(7\mid n+3\).
This is the system \(n\equiv2,3,4\) modulo \(3,5,7\).
We get \(n\equiv2\pmod3\), \(n\equiv3\pmod5\), \(n\equiv4\pmod7\). Checking or merging step by step gives \(n=53\). All solutions are \(n\equiv53\pmod{105}\), so the smallest positive \(n\) is \(53\).
Good practice with signs.