关于数的性质,希望能给诸位启发

kimpak

以下是引用rosemsem在2003-11-19 23:48:00的发言：
看到太多的关于整除，质数，等等的讨论。希望这道题的解题过程能给诸位以启发

N大于3的正整数，一个集合S{N+1，N+2，n+3。。。N+6}中质数个数最大是几？

positive integer n>3; S=[n+1, ..., n+6]

there are must be 3 even and 3 odd numbers in 6 consecutive numbers.
say n is an even number (or odd, does not matter)
so the odd # in S are n+1, n+3, n+5
then let us talk about if there is any prime # among those three,
let us say remainderof n has 3 possibilities if divided by 3 (0, 1, or 2)
if n =3a, (remainder=0), n+3 = 3a+3, not prime #
if n=3a+1, n+5=3a+6, not prime #
if n=3a+2, n+1 = 3a+3, not prime #

so at least one of the three could be dividied exactly by 3, so the the greatest prossible number of prime numbers is 2 in S.

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