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OlympiadBench / 1962 / Determine all triples (a,b,c) of positive integers for which ab−c,bc−a,…

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

Determine all triples

(a, b, c)

of positive integers for which

a b-c, b c-a

, and

c a-b

are powers of 2 . Explanation: A power of 2 is an integer of the form

2^{n}

, where

n

denotes some nonnegative integer.

Plain-text mathematical notation (without MathML)

Determine all triples (a,b,c) of positive integers for which ab−c,bc−a, and ca−b are powers of 2 .

Explanation: A power of 2 is an integer of the form 2^(n), where n denotes some nonnegative integer.

Original LaTeX notation

Determine all triples $(a, b, c)$ of positive integers for which $a b-c, b c-a$, and $c a-b$ are powers of 2 .

Explanation: A power of 2 is an integer of the form $2^{n}$, where $n$ denotes some nonnegative integer.

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1962
task_id: 43ae9a5e-2f50-501c-9f9e-b6fdd46c9534
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1962
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

initial import