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# Tag Archives: IMC

## [Soln] 2015 IMC Day 1 Problem 2

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

## 2015 IMC Day 1 Problem 2

## [Soln] 2015 IMC Day 1 Problem 3

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

## 2015 IMC Day 1 Problem 3

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

## [Soln] 2015 IMC Day 2 Problem 6

2015 IMC 2.6. Prove that

## 2015 IMC Day 2 Problem 6

2015 IMC 2.6. Prove that

## [Soln] 2015 IMC Day 1 Problem 1

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?