Blogs about: Olympiad Normal Problem Solving
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Putnam 2012 Day 2
1. Let be a class of functions from to that satisfies: (i) The functions and are in (ii) If and are in the functions and are in (iii) If and are in and for all then the function is in Prove that if an… more →
Beni Bogoşel's blog
Putnam 2012 Day 2
— 1 comment
wrote 4 months ago: 1. Let be a class of functions from to that satisfies: (i) The functions and are in (ii) If and are … more →
Putnam 2012 Day 1
wrote 4 months ago: 1. Let be real numbers in the open interval Show that there exist distinct indices such that are the … more →
Sum of some angles in a polygon
— 2 comments
wrote 5 months ago: Let be a convex polygon which has no two sides which are parallel. For each side consider the vertex … more →
Nice inequality similar to IMO 2011
wrote 6 months ago: Prove that Note the similarity to the IMO 2011 inequality, and surprisingly the same method works. P … more →
IMC 2012 Problem 6
wrote 9 months ago: Consider a polynomial Albert Einstein and Homer Simpson are playing the following game. In turn, the … more →
IMC 2012 Problem 5
wrote 10 months ago: Let be a rational number and let be a positive integer. Prove that the polynomial is irreducible in … more →
IMC 2012 Problem 4
wrote 10 months ago: Let be a continuously differentiable function that satisfies for all . Prove that for all . 45.56443 … more →
IMC 2012 Problem 3
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wrote 10 months ago: Given an integer , let be the group of permutation of the numbers . Two players and play the followi … more →
IMC 2012 Problem 2
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wrote 10 months ago: Let be a fixed positive integer. Determine the smallest positive rank of an matrix that has zeros al … more →
IMC 2012 Problem 1
wrote 10 months ago: For every positive integer denote denote the number of ways to express as a sum of positive integer. … more →
IMO 1996 Day 1
— 1 comment
wrote 11 months ago: Problem 1 We are given a positive integer and a rectangular board with dimensions . The rectangle is … more →
IMO 1995 Day 1
wrote 11 months ago: I decided to test myself on solving some IMO problems. Here are my solutions for IMO 1995 Day 1. Apa … more →
Balkan Mathematical Olympiad 2012 Problem 4
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wrote 1 year ago: Let be the set of positive integers. Find all functions such that the following conditions both hold … more →
Balkan Mathematical Olympiad 2012 Problem 3
wrote 1 year ago: Let be a positive integer. Let For each subset of , we write for the sum of all elements of , with t … more →
Balkan Mathematical Olympiad 2012 Problem 2
wrote 1 year ago: Prove that for all positive real numbers and . Balkan Mathematical Olympiad 2012 Problem 2 Solution: … more →
Balkan Mathematical Olympiad 2012 Problem 1
wrote 1 year ago: Let , and be points lying on a circle with centre . Assume that . Let be the point of intersection o … more →
Characterization of a normal matrix
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wrote 1 year ago: A matrix with complex entries is called normal if , where is the conjugate transpose of . Prove that … more →
SEEMOUS 2012 Problem 4
wrote 1 year ago: a) Compute . b) Let be an integer. Compute . a) Make the change of variable . The limit becomes Prov … more →
There isn't such a function
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wrote 1 year ago: Prove that there is no continuous function such that and . Proof: As noted in the first comment, a c … more →
