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f (x)+kx = m with at least one integral solution x for any m

Source: Czech and Slovak Match 1996 P4

October 1, 2017
number theoryFunction equationsinteger equationalgebra

Problem Statement

Decide whether there exists a function f:Zā†’Zf : Z \rightarrow Z such that for each k=0,1,...,1996k =0,1, ...,1996 and for any integer mm the equation f(x)+kx=mf (x)+kx = m has at least one integral solution xx.
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