`A = (3 + 1)(3^2 + 1)(3^4 + 1)(3^8 + 1)(3^16 + 1)(3^32 + 1)(3^64 + 1)(3^128 + 1)`
`<=> 2A = 2(3 + 1)(3^2 + 1)(3^4 + 1)(3^8 + 1)(3^16 + 1)(3^32 + 1)(3^64 + 1)(3^128 + 1)`
`= (3 - 1)(3 + 1)(3^2 + 1)(3^4 + 1)(3^8 + 1)(3^16 + 1)(3^32 + 1)(3^64 + 1)(3^128 + 1)`
`= (3^2 - 1)(3^2 + 1)(3^4 + 1)(3^8 + 1)(3^16 + 1)(3^32 + 1)(3^64 + 1)(3^128 + 1)`
`= (3^4 - 1)(3^4 + 1)(3^8 + 1)(3^16 + 1)(3^32 + 1)(3^64 + 1)(3^128 + 1)`
`= (3^8 - 1)(3^8 + 1)(3^16 + 1)(3^32 + 1)(3^64 + 1)(3^128 + 1)`
`= (3^16 - 1)(3^16 + 1)(3^32 + 1)(3^64 + 1)(3^128 + 1)`
`= (3^32 - 1)(3^32 + 1)(3^64 + 1)(3^128 + 1)`
`= (3^64 - 1)(3^64 + 1)(3^128 + 1)`
`= (3^128 - 1)(3^128 + 1)`
`= 3^256 - 1`
`=> A = (3^256 - 1)/2`
Vậy `A = (3^256 - 1)/2`
Áp dụng: `(x - y)(x + y) = x^2 - y^2`