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Re: HSC 2015 4U Marathon - Advanced Level What does the first line mean? Also, I think it's a good idea if symbols which are not seen in HSC exams are explained, unless they are abused here

Re: Harder HSC Papers How does question 8b) from the 2000 paper even make sense? Like how does P(1,0)=0? Why is it impossible for one to toss a fair coin and get a head followed by a tail?

Re: 2015 permutation X2 marathon Judging by the lack of responses to this question, I'd say that most people are confused by the wording. Can you provide an example as to what you mean by average (over S) of the number of fixed points in X of an arbitrary symmetry in S for instance?

Re: HSC 2015 4U Marathon - Advanced Level Suppose f(x) is a real valued function such that f(xy)+f(y-x)>=f(x+y). Prove that f(x)>=0

Re: 2015 permutation X2 marathon It might be a good idea to number the questions

Re: HSC 2015 4U Marathon - Advanced Level Show that 4m^2+17n^2 and 4n^2+17m^2 cannot be both be perfect squares, where n, and m are positive integers

Re: HSC 2015 4U Marathon ? Not sure what you mean here? Since S_k (-1) =0 as you claimed for all integers k, doesn't this mean that sigmaS_k(-1)*{m+1)Ck equals 0? (Since all the terms are zero, their sum is zero....am i wrong here?)

Re: HSC 2015 4U Marathon subbing in n=-1 gives 1+ sigmaS_k(-1)*{m+1)Ck=(-1+1)^m+1=0?? the LHS is 1 if S(-1)=0 for all k?

Re: HSC 2015 4U Marathon I could be misunderstanding, but from the definition of S_m (n) (in the first line of the question), does this mean that S_m (n) holds positive integer values only?

Re: HSC 2015 4U Marathon not sure whether i understand the problem, what does Sm(-1) look like? In fact, what does S_m (-n) look like? Is it (-1)^m+(-2)^m+....+(-n)^m?

Re: HSC 2015 4U Marathon - Advanced Level Uh......no. I think you should stop trying to sound smart/ bullshitting and start to post valid solutions.

Re: HSC 2015 4U Marathon - Advanced Level Now that Sy's question has been resolved, BUMP

Re: HSC 2015 4U Marathon - Advanced Level which conjecture are you referring to? If you mean the one in which u quoted, I think it has already been proven

Re: HSC 2015 4U Marathon - Advanced Level the coefficients are all real. and sorry, the root is x_i, not |x_i| (I failed my latex here).....

Re: HSC 2015 4U Marathon - Advanced Level \\ $ Consider a cubic polynomial $ P(x)=x^3+bx^2+cx+d $ .Show that $ |x_i| < 1 $ if and only if $ |bd-c| < 1-d^2 $ and $ |b+d| < |1+c| $where$ x_i$ is a root of the polynomial$

Re: HSC 2015 4U Marathon - Advanced Level also, ur solution for 1 is not a proper proof, read glittergal's previous posts to silent water and marinus

Re: HSC 2015 4U Marathon - Advanced Level what are you talking about. p(x) refers to a polynomial..........not p * (x-1).....

Re: HSC 2015 4U Marathon - Advanced Level you should attempt my problem!

Re: HSC 2015 4U Marathon - Advanced Level please post your solution. Are the ideas really motivable by a 4u student though? Here's something which CAN be done with mere 4u techniques. Find all real polynomials which satisfy p (x -1) *p (x+1)=p (x^2+1)