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Omni-MATH / Say that a polynomial with real coefficients in two variables, x,y, is …0. The balanced polynomials of degree at most 2009 form a vector space V over R. Find the dimension of V.

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problem

Say that a polynomial with real coefficients in two variables, x,yx,y, is \emph{balanced} if the average value of the polynomial on each circle centered at the origin is 00. The balanced polynomials of degree at most 20092009 form a vector space VV over R\mathbb{R}. Find the dimension of VV.
Plain-text mathematical notation (without MathML)
Say that a polynomial with real coefficients in two variables, x,y, is \emph{balanced} if
the average value of the polynomial on each circle centered at the origin is 0.
The balanced polynomials of degree at most 2009 form a vector space V over R.
Find the dimension of V.
Original LaTeX notation
Say that a polynomial with real coefficients in two variables, $x,y$, is \emph{balanced} if
the average value of the polynomial on each circle centered at the origin is $0$.
The balanced polynomials of degree at most $2009$ form a vector space $V$ over $\mathbb{R}$.
Find the dimension of $V$.

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Source and history

task_id
b1415986-576a-55d6-a818-cf526f0d1fb1
task_key
test--b1415986-576a-55d6-a818-cf526f0d1fb1
task_revision_id
1
config / split
/ test

Official source

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