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    Updated: 2024-11-10 08:06:36
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  • Dorin Marghidanu's Functional Equation

    Updated: 2024-11-10 08:06:33
    Determine all real functions f,for which f(1)=1 and f(x+y) = a^yf(x)+b^xf(y), where a,b are given real numbers, positive and different

  • An Integer Root of a Polynomial with Integer Coefficients

    Updated: 2024-11-10 08:06:32
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  • A Problem form the Short List of the 2018 JBMO

    Updated: 2024-11-10 08:06:31
    Let $a,b,c,d$ be real numbers with $0 ≤ a ≤ b ≤ c ≤ d.$ Prove that ab^3 + bc^3 + cd^3 + da^3 ≥ a^2b^2 + b^2c^2 + c^2d^2 + d^2a^2

  • An Inequality in Triangle for Side Lengths, Cycled in Two Ways

    Updated: 2024-11-10 08:06:30
    3(a/b + b/c + c/a - 1) ≥ 2(b/a + a/c + c/b)

  • Probability of Doubles

    Updated: 2024-11-10 08:06:29
    Show that if two dice are loaded with the same probability distribution, the probability of doubles is always at least 1/6

  • A Coin Tossing Surprise I

    Updated: 2024-11-10 08:06:28
    A fair coin is tossed repeatedly. What is the expected number of tosses before $HT$ shows up for the first time? What is the probability that $HT$ shows up before $TT?$

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