Problem
NT-B1-M04-P015 System Modulo 84
#15
★★★☆☆ Level 3 of 5
Find all \(x\pmod{84}\) such that \(x\equiv2\pmod3\), \(x\equiv3\pmod7\), \(x\equiv4\pmod{12}\).
Compare the first and third conditions modulo \(3\).
From \(x\equiv4\pmod{12}\), we get \(x\equiv1\pmod3\). But the first condition requires \(x\equiv2\pmod3\). Contradiction. Therefore there are no solutions.
A good compatibility check.