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标题: An 8th-grader number theory problem [打印本页]

作者: Xiangdang 时间: 2009-3-28 02:20
标题: An 8th-grader number theory problem

An 8th-grader math contest problem:

Prove that the unit-digits of a Mersenne Prime(for p >2, 2^p-1) will be either 1 or 7.

example:

p=17, 2^p-1=131,071

p = 31, 2^p-1=2,147,483,647

p.s. So far there are only 46 confirmed Mersenne primes. (Wikipedia)

作者: idiot94 时间: 2009-4-1 23:50
标题: 为什么没有人做了呢？这个题目比下面那个六年级的容易很多啊。。

不要被那个深奥的梅森素数吓着了，其实和它没有什么太大关系的。

作者: yma16 时间: 2009-4-8 04:19
标题: 回复：An 8th-grader number theory problem

Consider 2^n where n=3,4,5...

The last digits of the sequence are 8,6,2,4,8,6,2,4,... The 4 numbers repeat. So 2^p-1 cannot have 9 as the last digit. In order to get 3, 2^p must be 4. But when 2^n has 4 as the last digit, n is always even.

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