Problem
NT-B1-M08-P005 Equal Residues
#5
★☆☆☆☆ Level 1 of 5
Describe all \(x\) such that \(x\equiv3\pmod5\) and \(x\equiv3\pmod7\).
If a number has the same residue, subtract that residue.
The conditions mean that \(x-3\) is divisible by both \(5\) and \(7\). Since \(5\) and \(7\) are coprime, \(35\mid x-3\). Hence \(x\equiv3\pmod{35}\).
A useful short CRT case.