(2^2+1)×(2^4+1)×(2^8+1)×(2^16+1)X(2^32+1)因式分解,
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(2^2+1)×(2^4+1)×(2^8+1)×(2^16+1)X(2^32+1)因式分解,
![(2^2+1)×(2^4+1)×(2^8+1)×(2^16+1)X(2^32+1)因式分解,](/uploads/image/z/19512220-4-0.jpg?t=%282%5E2%2B1%29%C3%97%282%5E4%2B1%29%C3%97%282%5E8%2B1%29%C3%97%282%5E16%2B1%29X%282%5E32%2B1%29%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%2C)
(2+1)(2^2+1)(2^4+1)(2^8+1)……(2^32+1) =(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)……(2^32+1) =(2^2-1)(2^2+1)(2^4+1)(2^8+1)……(2^32+1) =(2^4-1)(2^4+1)(2^8+1)……(2^32+1) =(2^32-1)(2^32+1) =2^64-1