Tag Archives: 2015

[Soln] 2015 IMC Day 1 Problem 2

Posted on 1 Jun 2016 by kjytay

2015 IMC 1.2. For a positive integer , let be the number obtained by writing in binary and replacing every with and vice versa. For example, is in binary, so is in binary, therefore . Prove that When does equality … Continue reading →

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2015 IMC Day 1 Problem 2

Posted on 31 May 2016 by kjytay

2015 IMC 1.2. For a positive integer , let be the number obtained by writing in binary and replacing every with and vice versa. For example, is in binary, so is in binary, therefore . Prove that When does equality … Continue reading →

Posted in Intl/Regional, Undergraduate | Tagged , , | Leave a comment

[Soln] 2015 IMC Day 1 Problem 3

Posted on 30 May 2016 by kjytay

2015 IMC 1.3. Let , , and for . Determine whether or not is a rational number.

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2015 IMC Day 1 Problem 3

Posted on 29 May 2016 by kjytay

2015 IMC 1.3. Let , , and for . Determine whether or not is a rational number.

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[Soln] 2015 IMC Day 2 Problem 6

Posted on 28 May 2016 by kjytay

2015 IMC 2.6. Prove that

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2015 IMC Day 2 Problem 6

Posted on 27 May 2016 by kjytay

2015 IMC 2.6. Prove that

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[Soln] 2015 IMC Day 1 Problem 1

Posted on 20 May 2016 by kjytay

2015 IMC 1.1. For any integer and two matrices with real entries , that satisfy the equation Prove that . Does the same conclusion follow for matrices with complex entries?

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2015 IMC Day 1 Problem 1

Posted on 19 May 2016 by kjytay

2015 IMC 1.1. For any integer and two matrices with real entries , that satisfy the equation Prove that . Does the same conclusion follow for matrices with complex entries?

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[Soln] 2015 Spain MO Day 1 Problem 1

Posted on 19 Oct 2015 by kjytay

2015 Spain MO 1.1. On the graph of a polynomial with integer coefficients, two points are chosen with integer coordinates. Prove that if the distance between them is an integer, then the segment that connects them is parallel to the horizontal axis.

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2015 Spain MO Day 1 Problem 1

Posted on 18 Oct 2015 by kjytay

2015 Spain MO 1.1. On the graph of a polynomial with integer coefficients, two points are chosen with integer coordinates. Prove that if the distance between them is an integer, then the segment that connects them is parallel to the horizontal axis.

Posted in Grade 12, Spain | Tagged , , , | Leave a comment