MDantas's blog

Business Card — CERC 2008
By MDantas, 11 years ago, In English

Does anyone knows how to solve this problem ? http://cepc08.ii.uni.wroc.pl/cards.pdf

I've been trying to solve this problem, got some ideas but none of those ideas has really worked. Can anyone give me a hint ?

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11 years ago, # |
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YES is when exist such k, l, n, m ≥ 0 so
c = k × a + l × b
d = m × a + n × b.
NO otherwise.

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    11 years ago, # ^ |
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    What's the proof ? I could see this approach, but I wasn't sure if this is right.

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    11 years ago, # ^ |
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    counter-example:

    c=3 d=7 a=2 b=3

    c=0a+1b

    d=2a+1b

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      11 years ago, # ^ |
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      Yep, one more condition: a × b must divide c × d
      UPD This seems to be legit, but in paper I found another: (c = q × a or d = q × a) and (c = w × b or d = w × b).

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