benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Given an infinite sequence of numbers a₁,a₂,a₃,... . For each positive integer k there exists a positive integer t=t(k) such that a_(k)=a_(k+t)=a_(k+2t)=.... Is this sequence neces…

Problem

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

problem

Given an infinite sequence of numbers a1,a2,a3,...a_1, a_2, a_3,... . For each positive integer kk there exists a positive integer t=t(k)t = t(k) such that ak=ak+t=ak+2t=...a_k = a_{k+t} = a_{k+2t} =.... Is this sequence necessarily periodic? That is, does a positive integer TT exist such that ak=ak+Ta_k = a_{k+T} for each positive integer k?
Plain-text mathematical notation (without MathML)
Given an infinite sequence of numbers a₁,a₂,a₃,... . For each positive integer k there exists a positive integer t=t(k) such that a_(k)=a_(k+t)=a_(k+2t)=.... Is this sequence necessarily periodic? That is, does a positive integer T exist such that a_(k)=a_(k+T) for each positive integer k?
Original LaTeX notation
Given an infinite sequence of numbers $a_1, a_2, a_3,...$ . For each positive integer $k$ there exists a positive integer $t = t(k)$ such that $a_k = a_{k+t} = a_{k+2t} =...$. Is this sequence necessarily periodic? That is, does a positive integer $T$ exist such that $a_k = a_{k+T}$ for each positive integer k?

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
fa5bd268-1b92-5176-9616-9dd7438c6b9b
task_key
test--fa5bd268-1b92-5176-9616-9dd7438c6b9b
task_revision_id
1
config / split
/ test

Official source

initial import