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I am planing to get a pure math degree in university and become a mathematician. In uni, I found that there are two Bachelor of Mathematics and Bachelor of Sciences (which includes Mathematics). What is the difference between these two bachelor? If I want to become a mathematician, which one...

Re: Australian Maths Competition 2013 I think a,b,c are integers. I'm sorry, I don't really remember the problem.

Re: Australian Maths Competition 2013 I hope so ...

Re: Australian Maths Competition 2013 No, a,b,c are positive integers. I got 199 for the question a^{\sqrt b}=\sqrt{a^b}, almost forgot the case a=1...

Re: Australian Maths Competition 2013 Why do you imply n-m must be a perfect square? Oh, in the test, m only less than n.

I think it's ok to leave a like that. But you are right, all those 1's should be replaced by z.

Re: Australian Maths Competition 2013 OK. I remembered two questions: Given positive integer m<n,a,b,c and f(m)=0,f(n)=2016^2 where f(x)=ax^2+bx+c. How many values of n-m? How many pairs (a,b) of positive integers such that 1 \le a,b \le 100 and a^{\sqrt{b}}= \sqrt{a^b}.

Re: Australian Maths Competition 2013 I was up to f(126)=252 and then time-out. After the test, I realise that we can figure out the pattern (or prove by induction) that f(2^k \cdot (4n+1))=2^k(4n+3) and f(2^k(4n+3))=2^{k+1}(4n+1)

Re: Australian Maths Competition 2013 I think Q30 is an old question. I remembered this one from an AMO contest, may be. Although, I didn't get it during the test, I was out of time. :( Do you guys have answer for question 27,28,29 in senior division?