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Omni-MATH / Let m,n be positive integers. Find the minimum positive integer N which satisfies the following condition. If there exists a set S of integers that contains a complete residue syst…

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problem

Let m,nm,n be positive integers. Find the minimum positive integer NN which satisfies the following condition. If there exists a set SS of integers that contains a complete residue system module mm such that |S|=N| S | = N, then there exists a nonempty set A⊆SA \subseteq S so that $n\mid {\sum\limits_{x \in A} x }$.
Plain-text mathematical notation (without MathML)
Let m,n be positive integers. Find the minimum positive integer N which satisfies the following condition. If there exists a set S of integers that contains a complete residue system module m such that |S|=N, then there exists a nonempty set A⊆S so that $n\mid {\sum\limits_{x \in A} x }$.
Original LaTeX notation
Let $m,n$ be positive integers. Find the minimum positive integer $N$ which satisfies the following condition. If there exists a set $S$ of integers that contains a complete residue system module $m$ such that $| S | = N$, then there exists a nonempty set $A \subseteq S$ so that $n\mid {\sum\limits_{x \in A} x }$.

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Source and history

task_id
fe340c23-fde8-5416-8a02-1947aa4b47c2
task_key
test--fe340c23-fde8-5416-8a02-1947aa4b47c2
task_revision_id
1
config / split
/ test

Official source

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