Problem
NT-B1-M04-P016 Three Coprime Moduli
#16
★★★☆☆ Level 3 of 5
Solve \(x\equiv5\pmod8\), \(x\equiv2\pmod9\), \(x\equiv1\pmod5\).
First combine the first two congruences.
Let \(x=8a+5\). Modulo \(9\): \(8a+5\equiv2\), so \(-a\equiv-3\), hence \(a\equiv3\pmod9\). Thus \(x\equiv29\pmod{72}\). Now \(x=29+72t\), and modulo \(5\): \(4+2t\equiv1\), so \(2t\equiv2\), \(t\equiv1\pmod5\). We obtain \(x\equiv101\pmod{360}\).
Step-by-step merging of congruences.