Problem
NT-B1-M04-P019 Number of Solutions
#19
★★★☆☆ Level 3 of 5
Find all solutions of \(12x\equiv18\pmod{30}\).
\(\gcd(12,30)=6\).
Since \(6\mid18\), divide by \(6\): \(2x\equiv3\pmod5\). The inverse of \(2\) modulo \(5\) is \(3\), so \(x\equiv9\equiv4\pmod5\). Modulo \(30\): \(x\equiv4,9,14,19,24,29\).
The six solutions correspond to \(\gcd(12,30)=6\).