Problem
NT-B2-M09-P001 Two Residues
#1
★★☆☆☆ Level 2 of 5
Find all integers \(x\) such that \(x\equiv 4\pmod 9\) and \(x\equiv 7\pmod {11}\).
Set \(x=9t+4\).
Substitute: \(9t+4\equiv 7\pmod {11}\), so \(9t\equiv 3\pmod {11}\). Since \(9^{-1}\equiv 5\pmod {11}\), \(t\equiv 15\equiv 4\pmod {11}\). Thus \(x=9(11s+4)+4=99s+40\). The answer is \(x\equiv 40\pmod {99}\).
Basic technique of solving successively.