Librah
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Re: HSC 2015 4U Marathon - Advanced Level
Is irrelevant.Does it specify how many questions?
Is irrelevant.Does it specify how many questions?
Sorry for the lack of latex, on the train home right now and latexing on phone is annoying.
Has anyone solved this yet?Or is it the wording of the question that is throwing people off? Here is the exact wording of the question.
lol apparently that perms and combs q is an imo question according to integrand......doubt it was posted as a legit question. maybe glitter can do it thoughSorry for the lack of latex, on the train home right now and latexing on phone is annoying.
the problem is trivial for primes, so i'll just consider the composite numbers
Case 1: n = a*b, where a>b>1. Then, since a(b-1)-1>0, then ab-1>a>b>1. Thus, b and a divides (ab-1)!.
Case 2: n= a*a, where a>1. Then, since the smallest integer multiple of a which is greater than a is 2a, we need a^2-1 > 2a for a^2 to divide (a^2-1)!. Thus to find out which ones don't divide we consider where a^2-1<2a, and by solving the quadratic and taking the positive component we get a<1+root 2, and since a>1, the only integer value lying between this is a=2, meaning that n=4 does not divide 3!.
Hence, the set is n= all primes & n=4.
will have a look at the combs q later this week when i'm not so busy
Nope, its a semi-recent IMO Q3, which probably makes it v. hard indeed, and it's also in my weakest area of combinatorics. Will try it later if I am bored and have free time, but I'm not confident I would have much success.lol apparently that perms and combs q is an imo question according to integrand......doubt it was posted as a legit question. maybe glitter can do it though
Are you from Ruse? Did u ever go to tutoring in your high school years?Nope, its a semi-recent IMO Q3, which probably makes it v. hard indeed, and it's also in my weakest area of combinatorics. Will try it later if I am bored and have free time, but I'm not confident I would have much success.
No to both.Are you from Ruse? Did u ever go to tutoring in your high school years?
A start on this question:
I was hoping that the partial solution which I posted only an hour earlier would have prompted someone to join in before your final solution was posted.If there are any things which i haven't quite made clear pls let me know, then I'll explain when i next log on
Just came back from a 3 day camp and saw this, so I made have made some silly mistakes.
I think maybe there's a typo/error in the evaluation of the integral, since the part does not make sense dimensionally, but you got the right integral and working out before that, so well done.
Please notify me if there are silly algebra mistakes. Also, you have to wait for a bit for the latex to load (happened to me)
ah yep that was a typo, now fixed. (forgot a bracket)I think maybe there's a typo/error in the evaluation of the integral, since the part does not make sense dimensionally, but you got the right integral and working out before that, so well done.
Yep thought it was something like this (I didn't fully expand everything out when I did the Q).ah yep that was a typo, now fixed. (forgot a bracket)