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OlympiadBench / 1678 / Find all pairs (k,n) of positive integers for which 7^(k)−3^(n) divides…

Problem

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

question

Find all pairs

(k, n)

of positive integers for which

7^{k}-3^{n}

divides

k^{4}+n^{2}

Plain-text mathematical notation (without MathML)

Find all pairs (k,n) of positive integers for which 7^(k)−3^(n) divides k⁴+n².

Original LaTeX notation

Find all pairs $(k, n)$ of positive integers for which $7^{k}-3^{n}$ divides $k^{4}+n^{2}$.

answer type

Tuple

is multiple answer

false

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1678
task_id: a8fb9a70-9442-505f-a8a8-7a48215a31ad
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1678
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

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