Tag Archives: IMC

[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 →

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[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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