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2025 SSMO Relay Round 2 Problems/Problem 2

Revision as of 11:43, 9 September 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>T = TNYWR.</math> Let <math>x_1,x_2,\dots, x_{T}</math> be an increasing sequence of positive integers such that for every positive integer <math>1\le n...")
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Problem

Let $T = TNYWR.$ Let $x_1,x_2,\dots, x_{T}$ be an increasing sequence of positive integers such that for every positive integer $1\le n \le T,$ the sum $x_1+x_2+\cdots + x_n$ is a multiple of $n$. Find the smallest possible value of $x_{T} - x_1$.

Solution

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