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What's so special about 2014?

Hello Everybody,

Now half of the year has passed, and most of us (including me) will be sitting for various Maths Olympiads, taking place in the next half all around the globe. For me, its NMTC and RMO.

The point is- These Olympiads are, as we all are aware, going to use the number 2014 in most of their questions. Thus, it will be beneficial for us to know, beforehand, some of the special properties of 2014 and the questions which can be asked. I searched the net for some eccentricities of 2014, and I wasn't able to find one.

Thus, I'd like you to comment any peculiarities of the number 2014 which you know, and, of course, try to post all questions you know related to 2014 with a #2014 tag.

Note by Satvik Golechha
2 years, 9 months ago

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\(2014=2\cdot 19\cdot 53\). This can save you a lot of time. Daniel Liu · 2 years, 9 months ago

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@Daniel Liu The sum of the "non-obvious" prime factors of \(2014\) (prime factors you can't really tell just by looking at the number, which here are \(19\) and \(53\)) is the same as the sum of the non-obvious factors of \(2013\) (which are \(11\) and \(61\)).

I think I remember this fact being used on the AIME. Trevor B. · 2 years, 9 months ago

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Ahem! AFAIK, NMTC doesn't use any of the eccentric properties of any number. All they do is - employ this number in some form or the other in their questions! An example could be- They could describe a polynomial an ask you to find the \( f(2014)\). But, I'm sure they wouldn't ask such easy questions though ;) Krishna Ar · 2 years, 9 months ago

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@Krishna Ar Yes, but if they ask the sum of divisors of 2014, or something.....My intention was to collect as many questions about 2014 as I can...... Satvik Golechha · 2 years, 9 months ago

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@Satvik Golechha As I said before, "Questions would not be that easy". I'm sure, you know how to do it in a short way..Don't you? I will definitely help you in this endeavour though. Krishna Ar · 2 years, 9 months ago

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@Krishna Ar Yes, and again, my intention is to collect questions on 2014..... Satvik Golechha · 2 years, 9 months ago

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