Problem
NT-B1-M11-P010 Two Remainders
#10
★★☆☆☆ Level 2 of 5
Find all \(n\) such that \(n\equiv1\pmod3\) and \(n\equiv2\pmod5\).
Check numbers \(3k+1\) modulo \(5\).
Let \(n=3k+1\). Then \(3k+1\equiv2\pmod5\), so \(3k\equiv1\pmod5\), \(k\equiv2\pmod5\). Hence \(n=3(5t+2)+1=15t+7\). Answer: \(n\equiv7\pmod{15}\).
Short CRT review.