benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Determine whether there exists an infinite sequence of nonzero digits a₁,a₂,a₃,⋯ and a positive integer N such that for every integer k>N, the number (a_(k)a_(k−1)⋯a₁)¯ is a perfec…

Problem

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

problem

Determine whether there exists an infinite sequence of nonzero digits a1,a2,a3,⋯a_1 , a_2 , a_3 , \cdots and a positive integer NN such that for every integer k>Nk > N, the number akak−1⋯a1¯\overline{a_k a_{k-1}\cdots a_1 } is a perfect square.
Plain-text mathematical notation (without MathML)
Determine whether there exists an infinite sequence of nonzero digits a₁,a₂,a₃,⋯ and a positive integer N such that for every integer k>N, the number (a_(k)a_(k−1)⋯a₁)¯ is a perfect square.
Original LaTeX notation
Determine whether there exists an infinite sequence of nonzero digits $a_1 , a_2 , a_3 , \cdots $ and a positive integer $N$ such that for every integer $k > N$, the number $\overline{a_k a_{k-1}\cdots a_1 }$ is a perfect square.

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
7c5852e4-1dde-5b51-8630-9d2256fa426f
task_key
test--7c5852e4-1dde-5b51-8630-9d2256fa426f
task_revision_id
1
config / split
/ test

Official source

initial import