Problem
NT-B1-M08-P002 System Modulo \(5\) and \(7\)
#2
★☆☆☆☆ Level 1 of 5
Find the smallest positive \(x\) such that \(x\equiv4\pmod5\), \(x\equiv6\pmod7\).
Check numbers of the form \(5k+4\).
The numbers are \(4,9,14,19,24,29,34,\ldots\). The first congruent to \(6\) modulo \(7\) is \(34\). Thus \(x\equiv34\pmod{35}\).
Shows that searching one progression can be short.