Question

已知2的32次方＝a,求（2的2次方＋1）（2的4次方＋1）（2的8次方＋1）（2的16次方＋1）（2的32次方＋1）

Answer 1

2^32=a

(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)

=(1/3)(2^2-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)

=(1/3)(2^8-1)(2^8+1)(2^16+1)(2^32+1)

=(1/3)(2^16-1)(2^16+1)(2^32+1)

=(1/3)(2^32-1)(2^32+1)

=(1/3)[(2^32)^2-1]

=(1/3)(a^2-1)

=(a^2-1)/3