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Tuesday, October 12, 2010
10th Eötvös Competition Problems 1903
1. Prove that 2p-1(2p - 1) is perfect when 2p - 1 is prime. [A perfect number equals the sum of its (positive) divisors, excluding the number itself.] 2. α and β are real and a = sin α, b = sin β, c = sin(α+β). Find a polynomial p(x, y, z) with integer coefficients, such that p(a, b, c) = 0. Find all values of (a, b) for which there are less than four
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