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Omni-MATH / Determine the greatest positive integer k that satisfies the following property: The set of positive integers can be partitioned into k subsets A₁,A₂,…,A_(k) such that for all inte…

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problem

Determine the greatest positive integer kk that satisfies the following property: The set of positive integers can be partitioned into kk subsets A1,A2,…,AkA_1, A_2, \ldots, A_k such that for all integers n≥15n \geq 15 and all i∈{1,2,…,k}i \in \{1, 2, \ldots, k\} there exist two distinct elements of AiA_i whose sum is n.n. [i]
Plain-text mathematical notation (without MathML)
Determine the greatest positive integer k that satisfies the following property: The set of positive integers can be partitioned into k subsets A₁,A₂,…,A_(k) such that for all integers n≥15 and all i∈{1,2,…,k} there exist two distinct elements of A_(i) whose sum is n.

[i]
Original LaTeX notation
Determine the greatest positive integer $k$ that satisfies the following property: The set of positive integers can be partitioned into $k$ subsets $A_1, A_2, \ldots, A_k$ such that for all integers $n \geq 15$ and all $i \in \{1, 2, \ldots, k\}$ there exist two distinct elements of $A_i$ whose sum is $n.$

[i]

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Source and history

task_id
19a37311-eca0-5fd7-adac-e5c1deba0939
task_key
test--19a37311-eca0-5fd7-adac-e5c1deba0939
task_revision_id
1
config / split
/ test

Official source

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