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Don't praise that lord too loudly. If the only primes I knew about were 2, 3, 5, 7, 11, 13, I could make an equation 2x3x5x7x11x13+1=59x509

I suspect your calculator can only handle about 100 digits, not 12,978,189. Perhaps you could try a computer instead.

It's in the SMH now: http://www.smh.com.au/news/technology/13-milliondigit-prime-number-discovered/2008/09/29/1222650973074.html

A new Mersenne prime, 2^43,112,609-1 has been found on August 23, 2008 on Edson Smith's computer and is the largest known prime to date and has 12,978,189 digits 316,470,269,...,511 which you can download at http://prime.isthe.com/no.index/chongo/merdigit/long-m43112609/prime-c.html...

Here are some submissions: http://community.boredofstudies.org/attachment.php?attachmentid=16657 http://www.angelfire.com/ab7/fourunit/submission3.pdf http://news.ieu.asn.au/bos_stg6maths_ieuresp.doc http://www.mansw.nsw.edu.au/members/stage-6-review/MANSW-Advanced-Ext-1-Ext-2-response.pdf

All this nonsense of the Board of Studies telling teachers thou must not teach such-and-such before Year 11 is rubbish. The BOS rules stipulate the HSC cannot be completed over more than 5 years or less than 2 years. Therefore some Year 9 students can (and have done) Extension 2 Mathematics, for...

I don't know if you can say I'm good at AMC. I only did one question! But it'd be good to put up solutions here to the others. You might also like to look at mathlinks.ro for other competition level questions.

Yep. You are right. Cosine rule method works. Here it is:

Ta. I've attached a solution to Q30. Perhaps others may wish to add to this thread with complete solutions to all the other questions + alternative methods. e.g., I know of at least 4 other ways to solve Q30.

Links: 1959-2003: http://web.archive.org/web/20040401135340/www.kalva.demon.co.uk/imo.html 2004: http://sms.math.nus.edu.sg/Simo/IMO_Problems/04.pdf 2005: http://www.georgmohr.dk/imo/imo05sol.pdf 2006: http://olympiads.win.tue.nl/imo/imo2006/solutions.pdf 2007: <a...

Your Q1-7 are respectively Q20, 21, 24, 25, 26, 28, 30 in the 2007 Int. AMC. Answers are: 20. C 21. D 24. B 25. D 26. 503 28. 11 30. 898 Here are the official solutions for these questions:

The process for selecting the Australian team is described in more detail at http://www.amt.edu.au/amocprog.html Note that the selection processes are different for different countries. These other selection processes are described at...

Here is the article about it in today's Sydney Morning Herald: http://www.geocities.com/threeunitnotes/smh25.7.2008.jpg

Results for Australia (/42): Andrew Elvey Price 29 SILVER Giles Gardam 25 SILVER Paul Cheung 25 SILVER Max Menzies 24 SILVER Irene Lo 22 SILVER Sampson Wong 15 BRONZE Total: 140/252 Rank: 19/97 China came first (again! - surprise, surprise) - with 217 points - alas with 5 gold, 1 silver...

Here are a couple of youtubes more specifically on Terry Tao if you are interested: http://www.youtube.com/watch?v=p6ZUeQv2yFQ http://www.youtube.com/watch?v=zO7m7LS8dyg

YouTube of Australian Team: http://www.youtube.com/watch?v=9GNMIBA2Hec

Here are the questions http://www.angelfire.com/ab7/fourunit/imo2008.pdf (with questions 4-6 added)

For a dynamical system to be classified as chaotic, it must have the following properties: it must be sensitive to initial conditions, it must be topologically mixing, and its periodic orbits must be dense. Here are some links for chaos. http://mathworld.wolfram.com/Chaos.html...

Your teacher may not be aware that there are more than 1 definition. You'll get a different answer to no_arg's question depending on which definition you use.

But getting back to your example, I think it is a good one because the syllabus says y'' must be 0 at an inflection and change sign either side. Whilst that's OK for most examples, there will be some examples (like yours) for which it isn't true. So the syllabus's description does not suffice as...