Theo đầu bài ta có:
\(12\cdot\left(5^2+1\right)\cdot\left(5^4+1\right)\cdot\left(5^8+1\right)\cdot\left(5^{16}+1\right)\)
\(=\frac{24}{2}\cdot\left(5^2+1\right)\cdot\left(5^4+1\right)\cdot\left(5^8+1\right)\cdot\left(5^{16}+1\right)\)
\(=\frac{\left(5^2-1\right)\cdot\left(5^2+1\right)\cdot\left(5^4+1\right)\cdot\left(5^8+1\right)\cdot\left(5^{16}+1\right)}{2}\)
\(=\frac{\left(5^4-1\right)\cdot\left(5^4+1\right)\cdot\left(5^8+1\right)\cdot\left(5^{16}+1\right)}{2}\)
\(=\frac{\left(5^8-1\right)\cdot\left(5^8+1\right)\cdot\left(5^{16}+1\right)}{2}\)
\(=\frac{\left(5^{16}-1\right)\cdot\left(5^{16}+1\right)}{2}\)
\(=\frac{5^{32}-1}{2}\)