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题库 / Prep2008E1-DS-8
If n and m are positive integers, what is the remainder when ~$3^{(4n + 2 + m)}$~ is divided by 10 ?
(1) n = 2
(2) m = 1
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
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3的一次方／10，余数=3；二次方余数=9；三次方余数=7；四次方余数=1；4个数一个循环。
3的4n+2+m次方／10的余数=3的4n次方／10的余数+3的2次方／10的余数+3的m次方／10的余数，
因为余数是4个数1循环，所以3的4n次方／10的余数=3的四次方／10的余数=1，3的2次方／10的余数=9，只要m确定即可