Question

1+2的n次+2的96次是一个完全平方数,则n=_______

Answer 1

n=96÷2+1=49

或者n=(96-1)×2=190

(1+2^x)^2

=1+2*2^x+2^2x

=1+2^(x+1)+2^2x

2^2x=2^96或2^(x+1)=2^96

则n=x+1或n=2x