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Albanian BMO TST 2009 Question 3

Source:

June 4, 2010
functionmodular arithmeticEulernumber theory unsolvednumber theory

Problem Statement

For the give functions in N\mathbb{N}: (a) Euler's ϕ\phi function (ϕ(n)\phi(n)- the number of natural numbers smaller than nn and coprime with nn); (b) the σ\sigma function such that the σ(n)\sigma(n) is the sum of natural divisors of nn. solve the equation ϕ(σ(2x))=2x\phi(\sigma(2^x))=2^x.
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