Question

B = \(\left(5^2+1\right)\)\(\left(5^4+1\right)\)\(\left(5^8+1\right)\)\(\left(5^{16}+1\right)\) \(\left(5^{32}+1\right)\)

Answer 1

\(B=\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)

\(B=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right).\frac{1}{24}\)

\(B=\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right).\frac{1}{24}\)

\(B=\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right).\frac{1}{24}\)

\(B=\left(5^{16}-1\right)\left(5^{16}+1\right)\left(5^{32}+1\right).\frac{1}{24}\)

\(B=\left(5^{32}-1\right)\left(5^{32}+1\right).\frac{1}{24}\)

\(B=\left(5^{64}-1\right).\frac{1}{24}\)

\(B=\frac{5^{64}-1}{24}\)