benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let k be a given positive integer. Find all triples of positive integers a,b,c, such that a+b+c=3k+1, ab+bc+ca=3k²+2k. Slovakia

Problem

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

problem

Let kk be a given positive integer. Find all triples of positive integers a,b,ca, b, c, such that a+b+c=3k+1a + b + c = 3k + 1, ab+bc+ca=3k2+2kab + bc + ca = 3k^2 + 2k. Slovakia
Plain-text mathematical notation (without MathML)
Let k be a given positive integer. Find all triples of positive integers a,b,c, such that
a+b+c=3k+1,
ab+bc+ca=3k²+2k.

Slovakia
Original LaTeX notation
Let $k$ be a given positive integer. Find all triples of positive integers $a, b, c$, such that
$a + b + c = 3k + 1$,
$ab + bc + ca = 3k^2 + 2k$.

Slovakia

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
cc9ea7c0-5221-5d76-9933-6ecdbf81750c
task_key
test--cc9ea7c0-5221-5d76-9933-6ecdbf81750c
task_revision_id
1
config / split
/ test

Official source

initial import