1. Basic methods for solving functional equations ; 2. Cauchy equation and equations of the Cauchy type ; 3. Problems with solutions ; 4. Problems for independent ...

(IMO 1979, shortlist) Given a function f : R → R, if for every two real numbers x and y the equality f(xy+x+y) = f(xy)+ f(x)+ f(y) holds, prove that f(x+y) = f( ...

This page lists all of the catalogued problems involving functional equations in the AoPSWiki. ... 1968 IMO Problems/Problem 5 · 1972 IMO Problems/Problem 5 ...

1. Basic methods for solving functional equations ; 2. Cauchy equation and equations of the Cauchy type ; 3. Problems with solutions ; 4. Problems for independent ...

18 окт. 2016 г. · A typical functional equation will ask you to find all functions satisfying so-and-so property, for example: Example 1.1 (USAMO 2002). Find all ...

This problems involve explicit construction of functions, or inductive arguments. Problem 1. Let k be an even positive integer. Find the number of.

The students also write a series of challenging Olympiad-level problem papers, leading to selection of a team of six to go to the IMO. The bookets in this ...

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Inequalities, Integrals, Functional Equations; International Math Comp (IMC) 2022, Problem 1 ... A Challenging IMO Functional Equation Problem, IMO 1977, Problem ...

28 сент. 2023 г. · Remember that f(f(n))=f(n)+n must hold true for all numbers, so f(f(4))=f(4)+4, for example. So you can't just assign arbitrary values.