quasi
Posts:
9,097
Registered:
7/15/05
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Re: cotpi 41 - Counting locally prime numbers
Posted:
Feb 26, 2012 1:39 PM
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On Sun, 26 Feb 2012 20:31:39 +0530, cotpi <puzzles@cotpi.com> wrote:
>From a set of ten consecutive integers, a subset is chosen such
>that every integer that is coprime to every other integer in the
>set is present in the subset. What are the possible sizes of the
>subset?
Let S be a set of 10 consecutive positive integers.
The S contains 5 even integers and 5 odd integers.
Suppose T is a subset of S such that the elements of T are pairwise
coprime. Then T has at most one even elements, hence T contains at
most 6 elements.
That 6 is possible can be seen using
S = {10, 11, ..., 19}
T = {11, 13, 15, 16, 17, 19}
Of course any subset of T also satisfies the requirements, hence
the possible sizes are 0 through 6 inclusive.
quasi
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