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Italian Mathematical Olympiad 2008

Source: Problem 3

August 23, 2008
functioninductionfloor functionalgebra proposed

Problem Statement

Find all functions f:Zā†’R f: Z \rightarrow R that verify the folowing two conditions: (i) for each pair of integers (m,n) (m,n) with m<n m<n one has f(m)<f(n) f(m)<f(n); (ii) for each pair of integers (m,n) (m,n) there exists an integer k k such that f(m)\minus{}f(n)\equal{}f(k).
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