Javi
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 Apr 20 revised Prove that two sides are parallel in the reflection of an isosceles triangle Grammar Apr 20 asked Prove that two sides are parallel in the reflection of an isosceles triangle Feb 8 comment Pigeonhole principle and sequences problem Great! This is actually a problem I had to do in my discrete math exam last week. As I couldn't wait until we get the final grading I decided to post my approach here. Feb 8 accepted Pigeonhole principle and sequences problem Feb 8 revised Pigeonhole principle and sequences problem Clarify approach Feb 8 asked Pigeonhole principle and sequences problem Feb 1 awarded Editor Feb 1 revised Prove that $n=2^k -1$ is not a prime number, with $k=ab$. (Edit: $a\not=1$ and $b\not=1$) edited title Jan 31 awarded Scholar Jan 31 comment Prove that $n=2^k -1$ is not a prime number, with $k=ab$. (Edit: $a\not=1$ and $b\not=1$) Got it. Thank you very much. Jan 31 accepted Prove that $n=2^k -1$ is not a prime number, with $k=ab$. (Edit: $a\not=1$ and $b\not=1$) Jan 31 comment Prove that $n=2^k -1$ is not a prime number, with $k=ab$. (Edit: $a\not=1$ and $b\not=1$) I'm sorry I didn't state that $ab$ is a non-trivial factorisation. Jan 31 asked Prove that $n=2^k -1$ is not a prime number, with $k=ab$. (Edit: $a\not=1$ and $b\not=1$) Dec 28 comment Pigeonhole principle problem That's very simple! I was trying to fit in the pigeonhole principle as I could, but this is even more obvious. Dec 28 comment Pigeonhole principle problem Thank you so much! I only used the integer clue to assume that every day he trained a positive integer number of hours. Dec 28 comment Pigeonhole principle problem Ops. Sorry I saw the reference to using Latex after I posted the last comment. I'll do that next time. Thanks for the heads up. Dec 28 comment Pigeonhole principle problem OK. I think I got it now. We know that at least one pair is > 18. And as the problem states that he trained an integer number of hours, it has to be, at least, 19 hours. The grouping issue that Kannappan points out, can be solved if we group it like this: {1,12}, {2,3}, {4,5},{6,7},{8,9},{10,11}. This way we cover all the possible pairs and we can apply the same principle. Dec 28 comment Pigeonhole principle problem Wouldn't we need to leave {12,1} out? Dec 28 awarded Student Dec 28 asked Pigeonhole principle problem