Question

计算:2(3+1)(3的2次幂+1)(3的4次幂+1)……(3的16次幂+1)+1

Answer 1

2*(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)+1

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

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

=(3^4-1)(3^4+1)(3^8+1)(3^16+1)+1

.

=(3^16-1)(3^16+1)+1

=3^32-1+1

=3^32