benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let x₁=y₁=x₂=y₂=1, then for n≥3 let x_(n)=x_(n−1)y_(n−2)+x_(n−2)y_(n−1) and y_(n)=y_(n−1)y_(n−2)−x_(n−1)x_(n−2). What are the last two digits of |x₂₀₁₂| ?

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Let x1=y1=x2=y2=1x_{1}=y_{1}=x_{2}=y_{2}=1, then for n≥3n \geq 3 let xn=xn−1yn−2+xn−2yn−1x_{n}=x_{n-1} y_{n-2}+x_{n-2} y_{n-1} and yn=yn−1yn−2−xn−1xn−2y_{n}=y_{n-1} y_{n-2}- x_{n-1} x_{n-2}. What are the last two digits of |x2012|\left|x_{2012}\right| ?
Plain-text mathematical notation (without MathML)
Let x₁=y₁=x₂=y₂=1, then for n≥3 let x_(n)=x_(n−1)y_(n−2)+x_(n−2)y_(n−1) and y_(n)=y_(n−1)y_(n−2)−x_(n−1)x_(n−2). What are the last two digits of |x₂₀₁₂| ?
Original LaTeX notation
Let $x_{1}=y_{1}=x_{2}=y_{2}=1$, then for $n \geq 3$ let $x_{n}=x_{n-1} y_{n-2}+x_{n-2} y_{n-1}$ and $y_{n}=y_{n-1} y_{n-2}- x_{n-1} x_{n-2}$. What are the last two digits of $\left|x_{2012}\right|$ ?

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
0601efe3-460f-5bf6-81ce-e1bc5f5ccc26
task_key
test--0601efe3-460f-5bf6-81ce-e1bc5f5ccc26
task_revision_id
1
config / split
/ test

Official source

initial import