3(2^2+1)(2^4+1)(2^8+1)…(2^128+1)+1=?

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3(2^2+1)(2^4+1)(2^8+1)…(2^128+1)+1=?

3(2^2+1)(2^4+1)(2^8+1)…(2^128+1)+1=?
3(2^2+1)(2^4+1)(2^8+1)…(2^128+1)+1=?

3(2^2+1)(2^4+1)(2^8+1)…(2^128+1)+1=?
3=2^2-1
代入3(2^2+1)(2^4+1)(2^8+1)…(2^128+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)…(2^128+1)+1
=(2^4-1)(2^4+1)(2^8+1)…(2^128+1)+1
.
.
=(2^128-1)(2^128+1)+1
=(2^128)²-1+1
=2^256

原式=(2+1)(2*2+1)...+1, 乘以一个(2-1)值不变,但根据平方差公式a的平方-b的平方=(a+b)(a-b),原式=2^256-1+1=2^256

=(2^2^+1)^+1
=1

3(2^2+1)(2^4+1)(2^8+1)…(2^128+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)…(2^128+1)+1
=(2^4-1)(2^4+1)(2^8+1)…(2^128+1)+1
=(2^8-1)(2^8+1)……(2^128+1)+1
=(2^128-1)(2^128+1)+1
=2^256