964 - 1 = (932 + 1)(932 - 1) = ... = (932 + 1)(916 + 1)(98 + 1)(94 + 1)(92 + 1)(9 + 1)(9 - 1) > (932 + 1)(916 + 1)(98 + 1)(94 + 1)(92 + 1)(9 + 1)
964=(932+1).(932-1)
=(932+1)(916+1)(916-1)
=(932+1)(916+1)(98+1)(98-1)
=(932+1)(916+1)(98+1)(94+1)(94-1)
=(932+1)(916+1)(98+1)(94+1)(92+1)(92-1)
=(932+1)(916+1)(98+1)(94+1)(92+1)(9+1)(9-1)
Vì (932+1)(916+1)(98+1)(94+1)(92+1)(9+1)(9-1)>(932+1)(916+1)(98+1)(94+1)(92+1)(9+1)
=>964-1>(932+1)(916+1)(98+1)(94+1)(92+1)(9+1)
\(9^{64}-1\)
\(=\left(9^{32}+1\right)\left(9^{32}-1\right)\)
\(=\left(9^{32}+1\right)\left(9^{16}+1\right)\left(9^{16}-1\right)\)
\(...\)
\(=\left(9^{32}+1\right)\left(9^{16}+1\right)\left(9^8+1\right)\left(9^4+1\right)\left(9^2+1\right)\left(9+1\right)\left(9-1\right)\)
\(\Rightarrow9^{64}-1>\left(9+1\right)\left(9^2+1\right)\left(9^4+1\right)\left(9^8+1\right)\left(9^{16}+1\right)\left(9^{32}+1\right)\)