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f (92+ x) = f (92- x),f (19 .92+x) = f(19. 92-x),f (1992 + x) = f (1992 -x)

Source: Austrian - Polish 1992 APMC

May 7, 2020
functionalfunctional equationDivisorsalgebranumber theory

Problem Statement

A function f:Z→Zf: Z \to Z has the following properties: f(92+x)=f(92−x)f (92 + x) = f (92 - x) f(19⋅92+x)=f(19⋅92−x)f (19 \cdot 92 + x) = f (19 \cdot 92 - x) (19⋅92=174819 \cdot 92 = 1748) f(1992+x)=f(1992−x)f (1992 + x) = f (1992 - x) for all integers xx. Can all positive divisors of 9292 occur as values of f?
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