Chứng minh rằng: `2+2^2+2^3+2^4+...+2^60vdots3;7;15`
`A= (2+2^2)+(2^3+2^4)+...+(2^59+2^60)`
`A=2.(1+2)+2^3.(1+2)+...+2^59.(1+2)`
`A=2.3+2^3. 3+...+2^59. 3`
`A=3.(2+2^3+...+2^59)`
Vì `3vdots3 => 3.(2+2^3+...+2^59)vdots3`
`=>Avdots3`
`A= (2+2^2+2^3)+...+(2^58+2^59+2^60)`
`A=2.(1+2+2^2)+...+2^58.(1+2+2^2)`
`A=2.7+...+2^58. 7`
`A=7.(2+...+2^58)`
Vì `7vdots7 =>7.(2+...+2^58)vdots7`
`=>Avdots7`
`A= (2+2^2+2^3+2^4)+...+(2^57+2^58+2^59+2^60)`
`A=2.(1+2+2^2+2^3)+...+2^57.(1+2+2^2+2^3)`
`A=2. 15 +...+2^57. 15`
`A=15.(2+...+2^57)`
Vì `15vdots15=>15.(2+...+2^58)vdots15`
`=>Avdots15`
