乘以(2-1),再利用平方差公式!類似題目亦如此!
(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)……(2^512+1)+1
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)……(2^512+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)……(2^512+1)+1
……
=(2^512-1)(2^512+1)+1
=2^1024-1+1
=2^1024