benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Given any set A={a₁,a₂,a₃,a₄} of four distinct positive integers, we denote the sum a₁+a₂+a₃+a₄ by s_(A). Let n_(A) denote the number of pairs (i,j) with 1≤i<j≤4 for which …

Problem

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

problem

Given any set A={a1,a2,a3,a4}A = \{a_1, a_2, a_3, a_4\} of four distinct positive integers, we denote the sum a1+a2+a3+a4a_1 +a_2 +a_3 +a_4 by sAs_A. Let nAn_A denote the number of pairs (i,j)(i, j) with 1≤i<j≤41 \leq i < j \leq 4 for which ai+aja_i +a_j divides sAs_A. Find all sets AA of four distinct positive integers which achieve the largest possible value of nAn_A. [i]
Plain-text mathematical notation (without MathML)
Given any set A={a₁,a₂,a₃,a₄} of four distinct positive integers, we denote the sum a₁+a₂+a₃+a₄ by s_(A). Let n_(A) denote the number of pairs (i,j) with 1≤i<j≤4 for which a_(i)+a_(j) divides s_(A). Find all sets A of four distinct positive integers which achieve the largest possible value of n_(A).

[i]
Original LaTeX notation
Given any set $A = \{a_1, a_2, a_3, a_4\}$ of four distinct positive integers, we denote the sum $a_1 +a_2 +a_3 +a_4$ by $s_A$. Let $n_A$ denote the number of pairs $(i, j)$ with $1 \leq  i < j \leq 4$ for which $a_i +a_j$ divides $s_A$. Find all sets $A$ of four distinct positive integers which achieve the largest possible value of $n_A$.

[i]

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
346db62d-dcd5-5155-bbfc-8dde57a26e21
task_key
test--346db62d-dcd5-5155-bbfc-8dde57a26e21
task_revision_id
1
config / split
/ test

Official source

initial import