benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / What is the sum of all numbers q which can be written in the form q=(a)/(b) where a and b are positive integers with b≤10 and for which there are exactly 19 integers n that satisfy…

Problem

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

problem

What is the sum of all numbers qq which can be written in the form q=abq=\frac{a}{b} where aa and bb are positive integers with b≤10b \leq 10 and for which there are exactly 19 integers nn that satisfy q<n<q\sqrt{q}<n<q?
Plain-text mathematical notation (without MathML)
What is the sum of all numbers q which can be written in the form q=(a)/(b) where a and b are positive integers with b≤10 and for which there are exactly 19 integers n that satisfy √(q)<n<q?
Original LaTeX notation
What is the sum of all numbers $q$ which can be written in the form $q=\frac{a}{b}$ where $a$ and $b$ are positive integers with $b \leq 10$ and for which there are exactly 19 integers $n$ that satisfy $\sqrt{q}<n<q$?

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
cf2f5201-ea43-58b6-92cf-357703283146
task_key
test--cf2f5201-ea43-58b6-92cf-357703283146
task_revision_id
1
config / split
/ test

Official source

initial import