GMAT 数学题（8）

sdcar2010 · 发表于 2011-1-4 10:03:58

请问 ( 5⁹⁹⁹ + 6⁹⁹⁹ ) 的最小质因数是多少？为什么？

沉睡的巨人 · 发表于 2011-1-4 11:59:40

答案是2么？

sdcar2010 · 发表于 2011-1-4 12:01:40

答案是2么？

-- by 会员沉睡的巨人 (2011/1/4 11:59:40)

No way. 5^n is an odd number. 6^n is an even number. The sum of the two is an odd number.

cherry12345 · 发表于 2011-1-4 12:37:58

答案是3么?

sdcar2010 · 发表于 2011-1-4 12:41:28

答案是3么?

-- by 会员 cherry12345 (2011/1/4 12:37:58)

No. Because 5^n cannot be devided by 3 while 6^n definitely can. Therefore the sum of 5^999 and 6^999 cannot be devided by 3.

sdcar2010 · 发表于 2011-1-4 12:51:14

By now, you propably can figure out that 5 is not a factor, either, since 6^n cannot be devided by 5.

What about 7?

What about 11?

What about 13?

And why the above numbers can or cannot be the factor of the sum?

cherry12345 · 发表于 2011-1-4 13:01:13

What about 11? As 11 is the least common factor of 5 and 6.

sdcar2010 · 发表于 2011-1-4 13:02:57

What about 11? As 11 is the least common factor of 5 and 6.

-- by 会员 cherry12345 (2011/1/4 13:01:13)

I am curious about 11 as well. However, how can you prove that the sum of ( 5⁹⁹⁹ + 6⁹⁹⁹ ) can be devided by 11, or the sum of 5 and 6???

cherry12345 · 发表于 2011-1-4 13:06:33

I think 999 is an odd number, since 11 is the common factor of 5 and 6, so it could be devided by 11, or the sum of 5 and 6. I am not sure if this is right, as 7 and 13 cannot work.

心中的永恒 · 发表于 2011-1-4 15:36:47

是11

(a+b)^n-a^n-b^n必然有(a+b)的因子
根据杨辉三角

GMAT 数学题（8）

所属分类: GMAT考试

正在浏览此版块的会员 ()

浏览过的版块