Please, do not ask A-level questions.
1) Are you going to study Maths at Uni next year?
2) Do you want to do some extra Maths this summer?
If your answer to both questions is ``Yes!'', then I have the following suggestion.
We can make this a thread a place where interesting Maths problems of pre-Undergraduate/Undergraduate level are discussed.
The questions' difficulty can vary considerably, and they can be suggested by current undergraduate students, but the main focus must be on educational problems.
** I don't want people showing off with extremely difficult, not interesting and practically unsolvable with pre-Undergraduate/Undergraduate knowledge, questions. **
If you want to play this game, I have a few rules for a start.
 Post a question only if you believe it is of the right caliber and you have the complete solution.
 Indicate any required Undergraduate knowledge that people need to know in order to produce a solution to the given problem.
 Hints and solutions go in spoilers. In case they are required, the person who posted the question must provide them; with a reference to their origin.
List of problems offered by universities for practice during the summer.
List of suggested books that people have decided to spend time on over the summer:
List of additional resources that people suggested:
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
Cambridge Maths Tripos Part IA notes
Last edited by jack.hadamard; 24-07-2012 at 14:01.
(Original post by jack.hadamard)
such that for all
explicitly specifies the set of all natural numbers together with zero; i.e. the union of the natural numbers with the singleton that contains zero.
setting m=n=k=0 and re-arranging gives 0>=(f(0)-1)^2 so f(0)=1 therefore f(k)<=1 for all k. Similarly f(1)=1 so f(k)>=1 for all k. Combining these gives f(k)=k or f(x)=x as the only solution.
I like these function problems.
Last edited by james22; 01-07-2012 at 22:48.