Question

试说明：对于任何正整数n,2的n+4次方-2^n必能被3整除

Answer 1

2^(n+4) - 2^n

=2^n * 2^4 - 2^n

=2^n (2^4-1)

=2^n(16-1)

=15 * 2^n

=3 * 5 * 2^n

∴{ 2^(n+4) - 2^n } ÷ 3 = { 3 * 5 * 2^n } ÷ 3 = 5 * 2^n