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2 different functionals ff(f(n))=f(n+1) - f(n), f(f(n))=f(n+2) - f(n)

Source: 2009 Belarus TST 8.3

November 8, 2020
algebrafunctionalfunctional equation

Problem Statement

a) Does there exist a function f:N→Nf: N \to N such that f(f(n))=f(n+1)−f(n)f(f(n))=f(n+1) - f(n) for all n∈Nn \in N? b) Does there exist a function f:N→Nf: N \to N such that f(f(n))=f(n+2)−f(n)f(f(n))=f(n+2) - f(n) for all n∈Nn \in N?
I. Voronovich
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