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f(f(1)))= f(f(2))= f(f(3)), f(x) = ax^2 +bx + c

Source: 1998 Romania NMO IX p1

August 14, 2024
algebraquadraticstrinomial

Problem Statement

Find the integer numbers a,b,ca, b, c such that the function f:Rā†’Rf: R \to R, f(x)=ax2+bx+cf(x) = ax^2 +bx + c satisfies the equalities : f(f(1)))=f(f(2))=f(f(3))f(f(1) ))= f (f(2 ) )= f(f (3 ))
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