International Mathematics Competition for University Students

July 22 – 28 2018, Blagoevgrad, Bulgaria

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

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

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

Official IMC site

Problem 9

Problem 9. Determine all pairs \(\displaystyle P(x)\), \(\displaystyle Q(x)\) of complex polynomials with leading coefficient \(\displaystyle 1\) such that \(\displaystyle P(x)\) divides \(\displaystyle Q(x)^2+1\) and \(\displaystyle Q(x)\) divides \(\displaystyle P(x)^2+1\).

(Proposed by Rodrigo Angelo, Princeton University and Matheus Secco, PUC, Rio de Janeiro)

  Hint    Solution