Problem
NT-B1-M04-P018 Three Remainders
#18
★★★☆☆ Level 3 of 5
Find the smallest positive \(n\) such that \(n\equiv1\pmod2\), \(n\equiv2\pmod3\), \(n\equiv3\pmod5\).
First combine the conditions modulo \(2\) and \(3\).
The conditions \(n\equiv1\pmod2\), \(n\equiv2\pmod3\) give \(n\equiv5\pmod6\). Checking \(5,11,17,23,\ldots\), the first number congruent to \(3\) modulo \(5\) is \(23\). The answer is \(23\).
Simple construction from residues.