Question

Rut gon :P=12.(5²+1).(5⁴+1).(5⁸+1).(5¹⁶+1)

Answer 1

2P = 24.(5^2 + 1 )(5^4 + 1) ... (5^16 + 1)

2P = (5^2 - 1) (5^2 + 1) (5^4 + 1)  .. (5^16+1)

2P = (5^4 - 1 )(5^4 + 1 ) (5^8 + 1)

2P = (5^8 - 1 ) (5^8 + 1) (5^16 + 1)

2P = ( 5^ 16 - 1 ) 5^ 16 + 1)

2P = 5^32 - 1

P = (5^32 - 1) : 2

Answer 2

\(P=12.\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

\(\Rightarrow2P=24\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

\(\Leftrightarrow2P=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

\(\Leftrightarrow2P=\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

\(\Leftrightarrow2P=\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

\(\Leftrightarrow2P=\left(5^{16}-1\right)\left(5^{16}+1\right)\)

\(\Leftrightarrow2P=5^{32}-1\)

\(\Leftrightarrow P=\frac{5^{32}-1}{2}\)

 

Answer 3

2P = 24.(5^2 + 1 )(5^4 + 1) ... (5^16 + 1)

2P = (5^2 - 1) (5^2 + 1) (5^4 + 1)  .. (5^16+1)

2P = (5^4 - 1 )(5^4 + 1 ) (5^8 + 1)

2P = (5^8 - 1 ) (5^8 + 1) (5^16 + 1)

2P = ( 5^ 16 - 1 ) 5^ 16 + 1)

2P = 5^32 - 1

P = (5^32 - 1) : 2

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