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Omni-MATH / A sequence {a_(n)}_(n≥0) of real numbers satisfies the recursion a_(n+1)=a_(n)³−3a_(n)²+3 for all positive integers n. For how many values of a₀ does a₂₀₀₇=a₀ ?

Problem

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problem

A sequence {an}n≥0\left\{a_{n}\right\}_{n \geq 0} of real numbers satisfies the recursion an+1=an3−3an2+3a_{n+1}=a_{n}^{3}-3 a_{n}^{2}+3 for all positive integers nn. For how many values of a0a_{0} does a2007=a0a_{2007}=a_{0} ?
Plain-text mathematical notation (without MathML)
A sequence {a_(n)}_(n≥0) of real numbers satisfies the recursion a_(n+1)=a_(n)³−3a_(n)²+3 for all positive integers n. For how many values of a₀ does a₂₀₀₇=a₀ ?
Original LaTeX notation
A sequence $\left\{a_{n}\right\}_{n \geq 0}$ of real numbers satisfies the recursion $a_{n+1}=a_{n}^{3}-3 a_{n}^{2}+3$ for all positive integers $n$. For how many values of $a_{0}$ does $a_{2007}=a_{0}$ ?

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Source and history

task_id
b0dfe997-73a6-58e4-9850-22228d695ebf
task_key
test--b0dfe997-73a6-58e4-9850-22228d695ebf
task_revision_id
1
config / split
/ test

Official source

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