Problem
NT-B1-M10-P015 Divisibility of \(R_{6n}\)
#15
★★★☆☆ Level 3 of 5
Prove that the number consisting of \(6n\) ones is divisible by \(7\), \(11\), and \(13\).
Use \(R_6\mid R_{6n}\).
Since \(6\mid6n\), we have \(R_6\mid R_{6n}\). But \(R_6=111111=111\cdot1001\), and \(1001=7\cdot11\cdot13\). Hence \(R_{6n}\) is divisible by \(7\), \(11\), and \(13\).
Trains use of a previously proved lemma.