International Mathematics Competition
for University Students
2018

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IMC2018: Day 2, 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: Apply ViƩte Jumping.

    

IMC
2018

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