- 数学奥赛计算:(2*2+1)(2^*2^+1)<(2^*2
- 计算:(2*2+1)(2^*2^+1)<(2^*2^)^+1><(2^*2^)^*(2^*2^)^+1
- 第一种解法.
(2*2+1)(2^*2^+1)<(2^*2^)^+1><(2^*2^)^*(2^*2^)^+1>
=(2^+1)(2的4次方+1)<2的8次方+1><2的16次方+1>
=1/3*(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)
=1/3*(2^4-1))(2^4+1)(2^8+1)(2^16+1)
=1/3*(2^8-1)(2^8+1)(2^16+1)
=1/3*(2^16-1)(2^16+1)
=(2^32-1)/3
=31655765
第二种.
(2*2+1)(2^*2^+1)<(2^*2^)^+1><(2^*2^)^*(2^*2^)^+1>
=5*(4*4+1)<(4*4)^+1><(4*4)^*(4*4)^+1>
=5*17*<16^+1><16^*16^+1>
=85*<256+1><256*256+1>
=85*257*65537
=1431655765