Blogs about: Number Theory
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IMO phase II training Homework Solution
Here is my solution to the following problem given in IMO phase II training for the basic group: Problem(1): Find all positive integer solutions to: Proof: As I have said in l class, it is clear that … more →
Mathematics in HKCEE, HKAL, and Beyond
IMO phase II training Homework Solution
koopakoo wrote 1 month ago: Here is my solution to the following problem given in IMO phase II training for the basic group: Pro … more →
Pigeonhole Principle (1)
koopakoo wrote 11 months ago: When you place three apples into two boxes, then one of the boxes must contain at least two apples. … more →
Diophatine Equation (1)
koopakoo wrote 1 year ago: The following is a classical problem, which seems to be unknown to a lot of students, including the … more →
IMO 2008 Problem 3
koopakoo wrote 1 year ago: Prove that there are infinitely many positive integers such that has a prime divisor greater than … more →
Sum of Squares (1)
koopakoo wrote 1 year ago: It is a well known theorem by Fermat that any prime of the form can be written as a sum of two squar … more →
Leibniz's identity and beyond (1)
koopakoo wrote 1 year ago: We start with the following well-known identity: Let’s give a proof of this identity: Note tha … more →
HKIMO 2009 Selection Test 1 problem 2
koopakoo wrote 1 year ago: Here is the problem: Solve the following system of equations mod 37: At a glance, this really looks … more →
Hong Kong Selection Test 1 Problem 6 for IMO 2009
koopakoo wrote 1 year ago: The following question appeared in the selection test 1 for IMO 2009: For the equation: Show that th … more →
