Math problems

[Quang Le Minh <n1465236@student.fit.qut.edu.au>]

Hi guys,

I am very interested in solving math problems. So I have here some
classical  math problems for you:

* Prove the existance a number of the form: 19961996...1996 (This number
contains (2n+1) "1996"s) such that this number is divisible by 1997

* Find a 1-1 relation (with appropriate assumptions) that maps all the
points in a circle (including those points on the circle) to all the
points on a half plane (including its boundary). In other words, if
consider S is a set of all the point in and on a circle, R is a set of the
plane then
                       #S = #R

* Prove that in all sort of shapes that have constant "chu vi", the circle
has the maximum area.