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anonymous
 5 years ago
Fool's problem of the day ( on request of asnaseer), probably easy , I haven't thought much,
Let \(A = \{a_1, a_2 \cdots a_k\} \) be any set of \( k \) composite numbers such that
\(1 \le a_i \le 120 \) for all \(i\) such that \(1 \le i \le k\). Find the least value of \(k\) such
that there exists at least one pair \( (a_i, a_j) \), \(1\le i, j \le k\) in \(A\) which is not co
prime ?
anonymous
 5 years ago
Fool's problem of the day ( on request of asnaseer), probably easy , I haven't thought much, Let \(A = \{a_1, a_2 \cdots a_k\} \) be any set of \( k \) composite numbers such that \(1 \le a_i \le 120 \) for all \(i\) such that \(1 \le i \le k\). Find the least value of \(k\) such that there exists at least one pair \( (a_i, a_j) \), \(1\le i, j \le k\) in \(A\) which is not co prime ?

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I should go to bed now, Enjoy guys :)

asnaseer
 5 years ago
Best ResponseYou've already chosen the best response.2and thanks for the post

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You are always welcome :)

asnaseer
 5 years ago
Best ResponseYou've already chosen the best response.2isn't it k=2 > {1,2} are 1 and 2 considered to be co prime?

asnaseer
 5 years ago
Best ResponseYou've already chosen the best response.2ah!  of course  thx for pointing that out Mr.Math

asnaseer
 5 years ago
Best ResponseYou've already chosen the best response.2I thought 1 is coprime?

Mr.Math
 5 years ago
Best ResponseYou've already chosen the best response.0Two integers a and b are said to be coprime (also spelled coprime) or relatively prime if the only positive integer that evenly divides both of them is 1.

Mr.Math
 5 years ago
Best ResponseYou've already chosen the best response.0What about \(A=\{4,6\}?\), that's k=2.

asnaseer
 5 years ago
Best ResponseYou've already chosen the best response.2but 2 divides 4 and 6?

Mr.Math
 5 years ago
Best ResponseYou've already chosen the best response.0Yep, so they are NOT coprime.

asnaseer
 5 years ago
Best ResponseYou've already chosen the best response.2note to self: must learn to read the question properly!

asnaseer
 5 years ago
Best ResponseYou've already chosen the best response.2then your answer seems to be correct.

Mr.Math
 5 years ago
Best ResponseYou've already chosen the best response.0I think so, but that was too easy. Congrats on being a moderator, they couldn't have chosen any better :)

asnaseer
 5 years ago
Best ResponseYou've already chosen the best response.2thx Mr.Math  I am very humbled to have been chosen. FFM did say this is quite easy, but you are right  it seems TOO easy :)

Mr.Math
 5 years ago
Best ResponseYou've already chosen the best response.0Plus, he always says that even when it's TOO difficult. So I never trust his judgement. :D

asnaseer
 5 years ago
Best ResponseYou've already chosen the best response.2he he  yes  I concur. I'll have to mull over this one tomorrow. it's quite late here so I need to get some sleep. bye for now...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh well not that easy ;) Does \( K=2 \) or\( K=4 \) works for any coprime in\( 1\le a_i \le 120 \) ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Whenever I say that the problem is easy, it means that there exists a very short solution for that problem which may or may not use some well known theorems or results, and if I remember correctly I have posted only one too difficult problem here.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and now I have solved this one, I would say this is a easy problem ;)
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