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Omni-MATH / Find all polynomials f with real coefficients such that for all reals a,b,c such that ab+bc+ca=0 we have the following relations f(a−b)+f(b−c)+f(c−a)=2f(a+b+c).

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problem

Find all polynomials ff with real coefficients such that for all reals a,b,ca,b,c such that ab+bc+ca=0ab+bc+ca = 0 we have the following relations f(a−b)+f(b−c)+f(c−a)=2f(a+b+c). f(a-b) + f(b-c) + f(c-a) = 2f(a+b+c).
Plain-text mathematical notation (without MathML)
Find all polynomials f with real coefficients such that for all reals a,b,c such that ab+bc+ca=0 we have the following relations

f(a−b)+f(b−c)+f(c−a)=2f(a+b+c).
Original LaTeX notation
Find all polynomials $f$ with real coefficients such that for all reals $a,b,c$ such that $ab+bc+ca = 0$ we have the following relations

\[ f(a-b) + f(b-c) + f(c-a) = 2f(a+b+c). \]

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Source and history

task_id
1f30d9b4-30fa-5ff8-b467-9069af7d2d91
task_key
test--1f30d9b4-30fa-5ff8-b467-9069af7d2d91
task_revision_id
1
config / split
/ test

Official source

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