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OlympiadBench / 1988 / Let n≥2 be an integer, and let A_(n) be the set

Problem

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

question

Let

n \geqslant 2

be an integer, and let

A_{n}

be the set

A_{n}=\left\{2^{n}-2^{k} \mid k \in \mathbb{Z}, 0 \leqslant k<n\right\} .

Determine the largest positive integer that cannot be written as the sum of one or more (not necessarily distinct) elements of

A_{n}

Plain-text mathematical notation (without MathML)

Let n≥2 be an integer, and let A_(n) be the set

A_(n)={2^(n)−2^(k)∣k∈Z,0≤k<n}.

Determine the largest positive integer that cannot be written as the sum of one or more (not necessarily distinct) elements of A_(n).

Original LaTeX notation

Let $n \geqslant 2$ be an integer, and let $A_{n}$ be the set

$$
A_{n}=\left\{2^{n}-2^{k} \mid k \in \mathbb{Z}, 0 \leqslant k<n\right\} .
$$

Determine the largest positive integer that cannot be written as the sum of one or more (not necessarily distinct) elements of $A_{n}$.

answer type

Expression

is multiple answer

false

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1988
task_id: e2738dc1-81da-5798-b32a-5f0fa720334d
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1988
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

initial import