benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / Let P(x) be a polynomial with integer coefficients that satisfies P(17)=10 and P(24)=17. Given that P(n)=n+3 has two distinct integer solutions n₁ and n₂, find n₁ and n₂. (Give you…

Problem

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

problem

Let P(x)P(x) be a polynomial with integer coefficients that satisfies P(17)=10P(17)=10 and P(24)=17.P(24)=17. Given that P(n)=n+3P(n)=n+3 has two distinct integer solutions n1n_1 and n2,n_2, find n1n_1 and n2n_2. (Give your answer as a comma-separated list, in either order; for example, "2, 5" or "6, -3".)
Plain-text mathematical notation (without MathML)
Let P(x) be a polynomial with integer coefficients that satisfies P(17)=10 and P(24)=17. Given that P(n)=n+3 has two distinct integer solutions n₁ and n₂, find n₁ and n₂.

(Give your answer as a comma-separated list, in either order; for example, "2, 5" or "6, -3".)
Original LaTeX notation
Let $P(x)$ be a polynomial with integer coefficients that satisfies $P(17)=10$ and $P(24)=17.$ Given that $P(n)=n+3$ has two distinct integer solutions $n_1$ and $n_2,$ find $n_1$ and $n_2$.

(Give your answer as a comma-separated list, in either order; for example, "2, 5" or "6, -3".)

level

Level 4

type

Intermediate Algebra

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
4d2ccdc2-4199-541d-9176-0a9720c0ef1b
task_key
intermediate~5falgebra--test--4d2ccdc2-4199-541d-9176-0a9720c0ef1b
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import