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题库 / Prep2007E2-DS-162
If n is a positive integer and r is the remainder when n2 - 1 is divided by 8, what is the value of r ?
(1) n is odd.
(2) n is not divisible by 8.
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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条件一：n为奇数，
故设n=2k-1
n^2-1=(2k-1)^2-1
=4k(k-1)
因为 k(k-1)是相邻两个自然数的乘积.必然是2的倍数.所以原式4k(k-1)必然是8的倍数，故由条件一可知r=0.
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