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标题: primes [打印本页]

作者: yma16 时间: 2010-4-4 01:42
标题: primes

Any prime>3 can be written as 2n-1 or 2n+1 where n is an integer. Can it also written as mn-1 or mn+1, where m=3,4,5,6? (prove is needed for each m). If the answer is true, what is the smallest even m such that the question is not true and what is the smallest odd m such that the question is not true? Thanks.

作者: 6 and 5 时间: 2010-4-4 06:38
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作者: 5 and 6 时间: 2010-4-4 06:42
标题: 回复：primes

Sorry, They should be 5 and 8 respectively.

作者: yma16 时间: 2010-4-5 00:14
标题: Thanks. You are right.

Using these forms, it is easy to prove that the sum of twin primes can be divided by 12 when the primes are bigger than 3.

作者: 5 and 6 时间: 2010-4-6 02:52
标题: 回复：Thanks. You are right.

It is easy to show:

The sum of two consecutive odd integers that neither are divisible by 3 is divisible by 12.

www.ddhw.com

Is it more general than the above-mentioned result ?

作者: yma16 时间: 2010-4-7 18:39
标题: 回复：回复：Thanks. You are right.

I did not think about this way. Thank you again.

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