[求助]GWD31-04-Q4

答案是E。通过列几个例子知道n是偶数才行，但是怎么从题目条件推出n是偶数呢？谢谢！

For a nonnegative integer n, if the remainder is 1 when 2ⁿ is divided by 3, then which of the following must be true?

I.                   n is greater than zero.

II.                3ⁿ = (-3)ⁿ

III.             √2ⁿ  is an integer.

A.         I only

B.         II only

C.         I and II

D.         I and III

E.          II and III

I ) 当 n=0 时，2º
(2^0) = 1，满足条件；所以不对；

II
) 要想 3^n = (-3)^n, n 必须是偶数；

III)
要想 2^(n/2) 是正整数， n 必须上偶数。