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AIMO Past Papers

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brightsky:
Does anyone have any AIMO past papers (preferably with solutions) that they are willing to post up (excluding the practice paper on the AMT website)? Thanks. :)

Also, good luck to anyone doing the AIMO this Thursday.  :D

brightsky:
is a perfect square where is an integer. Find the largest possible value of . Any help appreciated.

brightsky:
Are you able to give me a scanned copy of just 2007-2008? I'm working on them now.  ::)

brightsky:

--- Quote from: AzureBlue on August 11, 2010, 08:20:52 pm ---
--- Quote from: brightsky on August 11, 2010, 08:11:28 pm --- is a perfect square where is an integer. Find the largest possible value of . Any help appreciated.

--- End quote ---
AIMO 2007 Q7.

Suppose x^2-19x+94 = m^2 where m is a non-neg integer. Then x^2-19x+94-m^2 = 0

Go from there.

--- End quote ---

Ah, solved. Thanks Azure!

Next:

5. Find where and are non-zerp solutions of the system of equations:




9. Find a prime, p, with the property that for some larger prime number, q, both 2q - p and 2q + p are prime numbers. Prove that there is only one such prime p.

kamil9876:
Probably not the best way, but the equations given are ugly anyway :P:

Subtract from the first equation the second times 5. You get:








So either x=0. y=5x, or y=17, lolz. Now you can plug these in to the original equation to see what u get in each case.

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