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Omni-MATH / Let a₀=−2,b₀=1, and for n≥0, let begin{aligned} & a_{n+1}=a_{n}+b_{n}+sqrt{a_{n}^{2}+b_{n}^{2}} & b_{n+1}=a_{n}+b_{n}-sqrt{a_{n}^{2}+b_{n}^{2}} end{aligned} Find a₂₀₁₂.

Problem

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problem

Let a0=−2,b0=1a_{0}=-2, b_{0}=1, and for n≥0n \geq 0, let $$\begin{aligned} & a_{n+1}=a_{n}+b_{n}+\sqrt{a_{n}^{2}+b_{n}^{2}} \\ & b_{n+1}=a_{n}+b_{n}-\sqrt{a_{n}^{2}+b_{n}^{2}} \end{aligned}$$ Find a2012a_{2012}.
Plain-text mathematical notation (without MathML)
Let a₀=−2,b₀=1, and for n≥0, let $$\begin{aligned} & a_{n+1}=a_{n}+b_{n}+\sqrt{a_{n}^{2}+b_{n}^{2}} \\ & b_{n+1}=a_{n}+b_{n}-\sqrt{a_{n}^{2}+b_{n}^{2}} \end{aligned}$$ Find a₂₀₁₂.
Original LaTeX notation
Let $a_{0}=-2, b_{0}=1$, and for $n \geq 0$, let $$\begin{aligned} & a_{n+1}=a_{n}+b_{n}+\sqrt{a_{n}^{2}+b_{n}^{2}} \\ & b_{n+1}=a_{n}+b_{n}-\sqrt{a_{n}^{2}+b_{n}^{2}} \end{aligned}$$ Find $a_{2012}$.

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Source and history

task_id
efc6b385-2822-50e8-9366-88561a7a4c66
task_key
test--efc6b385-2822-50e8-9366-88561a7a4c66
task_revision_id
1
config / split
/ test

Official source

initial import