Problem
NT-B1-M08-P001 System Modulo \(4\) and \(5\)
#1
★☆☆☆☆ Level 1 of 5
Find the smallest positive \(x\) such that \(x\equiv1\pmod4\), \(x\equiv2\pmod5\).
Check the numbers \(1,5,9,13,17,\ldots\).
The numbers \(x\equiv1\pmod4\) are \(1,5,9,13,17,\ldots\). The first with residue \(2\) modulo \(5\) is \(17\). The answer is \(17\), and all solutions are \(x\equiv17\pmod{20}\).
Basic hand CRT.