Problem
NT-B2-M09-P005 Prescribed Residues
#5
★★☆☆☆ Level 2 of 5
Construct a positive \(N\) such that \(N\equiv 2\pmod 3\), \(N\equiv 4\pmod 5\), \(N\equiv 6\pmod 7\).
Notice that all residues are \(-1\) modulo their moduli.
The conditions mean \(N\equiv -1\pmod 3\), \(N\equiv -1\pmod 5\), \(N\equiv -1\pmod 7\). Hence \(N\equiv -1\pmod {105}\). For example, \(N=104\).
Useful for training students to see a common pattern rather than solve mechanically every time.