Problem 004

Does there exist a bijective map such that

Problem 003

Prove that

for all real number each different from 1, and satisfying
IMO 2008

Problem 002

Determine all functions defined on the set of rational number that take rational values for which

for each and .
CMO

Problem 001

A sequence is generated by recurrence formula

,

for, with . Prove that is integer valued for all integer .
Virginia Tech Regional Mathematics Contest, 1983

Announcement for All

By this time I want to give some problems in Mathematics. The problem is always about Mathematics. I will let you to solve the problems. You can solve the problem, and send the solutions by email. In rtf file, please.
If somebody want to give me suggestion about problems want to be published in this blog, you can send me the problem, then I will write the problems in this blog.
Your answer, problem, and other suggestions can be sent to rosid_uny@yahoo.co.id
Thank you very much