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OlympiadBench / 1737 / Find all pairs (m,n) of nonnegative integers for which

Problem

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

answer type

Tuple

is multiple answer

true

language

English

question

Find all pairs

(m, n)

of nonnegative integers for which

$$
m^{2}+2 \cdot 3^{n}=m\left(2^{n+1}-1\right)
\tag{1}
$$

Plain-text mathematical notation (without MathML)

Find all pairs (m,n) of nonnegative integers for which

$$
m^{2}+2 \cdot 3^{n}=m\left(2^{n+1}-1\right)
\tag{1}
$$

Original LaTeX notation

Find all pairs $(m, n)$ of nonnegative integers for which

$$
m^{2}+2 \cdot 3^{n}=m\left(2^{n+1}-1\right)
\tag{1}
$$

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1737
task_id: 1c060b08-9779-5e35-b2ca-6f2277d52f44
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1737
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

initial import