benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Isabella writes the expression √(d) for each positive integer d not exceeding 8 ! on the board. Seeing that these expressions might not be worth points on HMMT, Vidur simplifies ea…

Problem

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

problem

Isabella writes the expression d\sqrt{d} for each positive integer dd not exceeding 8 ! on the board. Seeing that these expressions might not be worth points on HMMT, Vidur simplifies each expression to the form aba \sqrt{b}, where aa and bb are integers such that bb is not divisible by the square of a prime number. (For example, 20,16\sqrt{20}, \sqrt{16}, and 6\sqrt{6} simplify to 25,412 \sqrt{5}, 4 \sqrt{1}, and 161 \sqrt{6}, respectively.) Compute the sum of a+ba+b across all expressions that Vidur writes.
Plain-text mathematical notation (without MathML)
Isabella writes the expression √(d) for each positive integer d not exceeding 8 ! on the board. Seeing that these expressions might not be worth points on HMMT, Vidur simplifies each expression to the form a√(b), where a and b are integers such that b is not divisible by the square of a prime number. (For example, √(20),√(16), and √(6) simplify to 2√(5),4√(1), and 1√(6), respectively.) Compute the sum of a+b across all expressions that Vidur writes.
Original LaTeX notation
Isabella writes the expression $\sqrt{d}$ for each positive integer $d$ not exceeding 8 ! on the board. Seeing that these expressions might not be worth points on HMMT, Vidur simplifies each expression to the form $a \sqrt{b}$, where $a$ and $b$ are integers such that $b$ is not divisible by the square of a prime number. (For example, $\sqrt{20}, \sqrt{16}$, and $\sqrt{6}$ simplify to $2 \sqrt{5}, 4 \sqrt{1}$, and $1 \sqrt{6}$, respectively.) Compute the sum of $a+b$ across all expressions that Vidur writes.

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
efd50de5-ac49-5908-be77-c148143b3ad0
task_key
test--efd50de5-ac49-5908-be77-c148143b3ad0
task_revision_id
1
config / split
/ test

Official source

initial import