`11^10-1`
`=(11^5)^2-1`
`=(11^5-1)(11^5+1)`
`=(11-1)(11^4+11^3+11^2+11+1)(11+1)(11^4-11^3+11^2-11+1)`
`=10.12.(11^14+11^3+11^2+11+1)(11^4-11^3+11^2-11+1)`
Vì
`11^4+11^3+11^2+11+1=\overline{...1}+\overline{....1}+\overline{.....1}+\overline{....1}+\overline{....1}=\overline{....5}\vdots 5`
Mà `12\vdots 12`
`10\vdots 10`
`\to 10.12.(11^4+11^3+11^2+11+1)(11^4-11^3+11^2-11+1)\vdots 100`
`\to 10.12.(11^4+11^3+11^2+11+1)(11^4-11^3+11^2-11+1)\vdots 100`
Hay `11^{10}-1\vdots 100`