International Mathematics Competition for University Students

July 22 – 28 2018, Blagoevgrad, Bulgaria

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Ivan is Watching You
Ivan's Office

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

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

Official IMC site

Problem 4

Problem 4. Find all differentiable functions \(\displaystyle f:(0,\infty)\to\RR\) such that

\(\displaystyle f(b)-f(a)=(b-a)f'\left(\sqrt{ab}\right) \quad \text{for all} \quad a,b>0. \tag2 \)

(Proposed by Orif Ibrogimov, National University of Uzbekistan)

  Hint    Solution