Đặt [tex]\overline{abc}=11m+k[/tex] (m, k nguyên dương)
và [tex]\overline{xyz}=11n+k[/tex] (m,k nguyên dương
ta có: [tex]\overline{abcxyz}=1000.\overline{abc}+\overline{xyz}=1000(11m+k)+11n+k=11000m+1000k+11n+k=11000m++11n+1001k=11(1000m+n+91k)\vdots 11[/tex]