Question

Sn=3^n 求证 当n为偶数时 Sn-4n-1能被64整除

Answer 1

n=2k

3^2k-1-8k=9^k-1-8k=(9-1)(9^(k-1)+9^(k-2)+...1)-8k

=8(9^(k-1)+9^(k-2)+...1-k)

=8((8+1)^(k-1)+(8+1)^(k-2)+...1-k)

=8(8a+1+8b+1+8c+1+...+1-k)

=8(8(a+b+c+...)

=64x

能被64整除