International Mathematics Competition for University Students

July 31 – August 6 2017, Blagoevgrad, Bulgaria

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Ivan is Watching You

Day 1
    Problem 1
    Problem 2
    Problem 3
    Problem 4
    Problem 5

Day 2
    Problem 6
    Problem 7
    Problem 8
    Problem 9
    Problem 10

Results
    Individuals
    Teams
    Leaders

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    Day 1 questions
    Day 1 solutions
    Day 2 questions
    Day 2 solutions
    Closing Ceremony
        Presentation

Official IMC site

Problem 1

1. Determine all complex numbers $\lambda$ for which there exist a positive integer $n$ and a real $n\times n$ matrix $A$ such that $A^2=A^T$ and $\lambda$ is an eigenvalue of $A$.

Proposed by: Alexandr Bolbot, Novosibirsk State University

  Hint    Solution