Problem
NT-B1-M04-P017 Solve the Linear Congruence First
#17
★★★☆☆ Level 3 of 5
Find all \(x\pmod{60}\) such that \(4x\equiv8\pmod{12}\) and \(x\equiv3\pmod5\).
First solve \(4x\equiv8\pmod{12}\).
The congruence \(4x\equiv8\pmod{12}\), after division by \(4\), gives \(x\equiv2\pmod3\). Combine with \(x\equiv3\pmod5\). Among \(3,8,13,\ldots\) modulo \(5\), the number \(8\equiv2\pmod3\). Hence \(x\equiv8\pmod{15}\). Modulo \(60\), this gives \(x\equiv8,23,38,53\).
Teaches not to forget the requested final modulus.