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Omni-MATH / 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 necessa…

Problem

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problem

Let n≥2n \ge 2 be an integer, and let AnA_n be the set An={2n−2k∣k∈Z,0≤k<n}.A_n = \{2^n - 2^k\mid k \in \mathbb{Z},\, 0 \le k < n\}. Determine the largest positive integer that cannot be written as the sum of one or more (not necessarily distinct) elements of AnA_n . [i]
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) .

[i]
Original LaTeX notation
Let $n \ge 2$ be an integer, and let $A_n$ be the set \[A_n = \{2^n  - 2^k\mid k \in \mathbb{Z},\, 0 \le k < n\}.\] Determine the largest positive integer that cannot be written as the sum of one or more (not necessarily distinct) elements of $A_n$ .

[i]

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Source and history

task_id
968eba26-113e-5439-bb5c-83cd9508927c
task_key
test--968eba26-113e-5439-bb5c-83cd9508927c
task_revision_id
1
config / split
/ test

Official source

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