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OlympiadBench / 1738 / Find the smallest number n such that there exist polynomials …

Problem

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

answer type

Numerical

is multiple answer

false

language

English

question

Find the smallest number

n

such that there exist polynomials

f_{1}, f_{2}, \ldots, f_{n}

with rational coefficients satisfying

x^{2}+7=f_{1}(x)^{2}+f_{2}(x)^{2}+\cdots+f_{n}(x)^{2} .

Plain-text mathematical notation (without MathML)

Find the smallest number n such that there exist polynomials f₁,f₂,…,f_(n) with rational coefficients satisfying

x²+7=f₁(x)²+f₂(x)²+⋯+f_(n)(x)².

Original LaTeX notation

Find the smallest number $n$ such that there exist polynomials $f_{1}, f_{2}, \ldots, f_{n}$ with rational coefficients satisfying

$$
x^{2}+7=f_{1}(x)^{2}+f_{2}(x)^{2}+\cdots+f_{n}(x)^{2} .
$$

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1738
task_id: 6bfee446-da6a-57f1-9196-6ccef582608a
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1738
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

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