Problem
NT-B1-M04-P012 Smallest Number from Two Remainders
#12
★★☆☆☆ Level 2 of 5
Find the smallest positive number that leaves remainder \(2\) modulo \(5\) and remainder \(3\) modulo \(7\).
Check \(2,7,12,17,\ldots\).
Numbers of the form \(5k+2\) are \(2,7,12,17,\ldots\). The first one with residue \(3\) modulo \(7\) is \(17\). The answer is \(17\).
Small word problem on a system of congruences.