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MATH / A set S is constructed as follows. To begin, S={0,10}. Repeatedly, as long as possible, if x is an integer root of some nonzero polynomial a_(n)x^(n)+a_(n−1)x^(n−1)+…+a₁x+a₀ for so…

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problem

A set SS is constructed as follows. To begin, S={0,10}S = \{0,10\}. Repeatedly, as long as possible, if xx is an integer root of some nonzero polynomial anxn+an−1xn−1+…+a1x+a0a_{n}x^n + a_{n-1}x^{n-1} + \dots + a_{1}x + a_0 for some n≥1n\geq{1}, all of whose coefficients aia_i are elements of SS, then xx is put into SS. When no more elements can be added to SS, how many elements does SS have?
Plain-text mathematical notation (without MathML)
A set S is constructed as follows. To begin, S={0,10}. Repeatedly, as long as possible, if x is an integer root of some nonzero polynomial a_(n)x^(n)+a_(n−1)x^(n−1)+…+a₁x+a₀ for some n≥1, all of whose coefficients a_(i) are elements of S, then x is put into S. When no more elements can be added to S, how many elements does S have?
Original LaTeX notation
A set $S$ is constructed as follows. To begin, $S = \{0,10\}$. Repeatedly, as long as possible, if $x$ is an integer root of some nonzero polynomial $a_{n}x^n + a_{n-1}x^{n-1} + \dots + a_{1}x + a_0$ for some $n\geq{1}$, all of whose coefficients $a_i$ are elements of $S$, then $x$ is put into $S$. When no more elements can be added to $S$, how many elements does $S$ have?

level

Level 4

type

Intermediate Algebra

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task_id
9811106e-1d10-5b88-ae31-2d7eebb6ba75
task_key
intermediate~5falgebra--test--9811106e-1d10-5b88-ae31-2d7eebb6ba75
task_revision_id
1
config / split
intermediate_algebra / test

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