Question

sao sanh A=\(\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\) ) voi B=\(3^{32}\)

Answer 1

A*2=(3-1)*(3+1)*(3^2+1)*....*(3^16+1)

A*2=(3^2-1)*(3^2+1)*(3^4+1)....*(3^16+1)

A*2=((3^4)^2-1^2)*(3^4+1)......*(3*16+1)

2*A=(3^8-1)*...(3^16+1)

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Answer 2

nhân vào A 3^2-1

Answer 3

\(B=3^{32}-1=\left(3^{16}+1\right)\left(3^{16}-1\right)\)

\(=\left(3^{16}+1\right)\left(3^8+1\right)\left(3^8-1\right)\)

\(=\)\(\left(3^{16}+1\right)\left(3^8+1\right)\left(3^4+1\right)\left(3^4-1\right)\)

\(=\left(3^{16}+1\right)\left(3^8+1\right)\left(3^{\text{4}}+1\right)\left(3^2+1\right)\left(3^2-1\right)\)

\(=\left(3^{16}+1\right)\left(3^8+1\right)\left(3^4+1\right)\left(3^2+1\right)\left(3+1\right)\left(3-1\right)\)

\(=2\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)

\(B=2A\)

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