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3 comments:
Article aside, what is up with this portrait on the Tehelka page?
Vik, quite a likeness, isn't it? I sent them a photo once to use; they seem to have used that to draw this line sketch, though in mirror image!
nothing to do with the post, but since you like puzzles, here's one:
N is some integer. You pick some (N + 1) numbers from 1, 2, ..., 2N. Prove that in any such pick, there are always two numbers which are coprime. (Two numbers are coprime if their only common divisor is 1.)
Hint: First try to see how you can pick N numbers from 1, 2, .., 2N in such a way that no two are coprime. You will see that there is no space to put in the (N+1)th number coprime to all the others.
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