Calculation: (2 + 1) ({2} ^ {2} + 1) ({2} ^ {4} + 1) ({2} ^ {8} + 1)... ({2} ^ {256} + 1)

Calculation: (2 + 1) ({2} ^ {2} + 1) ({2} ^ {4} + 1) ({2} ^ {8} + 1)... ({2} ^ {256} + 1)

Answer: add factor (2-1) and reuse the square difference formula
（2+1）（{2}^{2}+1）（{2}^{4}+1）（{2}^{8}+1）...（{2}^{256}+1）
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1).(2^256+1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1).(2^256+1)
=(2^4-1)(2^4+1)(2^8+1).(2^256+1)
=(2^8-1)(2^8+1).(2^256+1)
=(2^16-1).(2^256+1)
=2^512 -1

Elden Ring Premiere

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