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Difference between revisions of "2022 SSMO Speed Round Problems/Problem 10"

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==Problem==
  
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Let <math>S = \{2,7,15,26,....\}</math> be the set of all numbers for which the <math>i^{th}</math> element in <math>S</math> is the sum of the <math>i^{th}</math> triangular number and the <math>i^{th}</math> positive perfect square. Let <math>T</math> be the set which contains all unique remainders when the elements in <math>S</math> are divided by <math>2022</math>. Find the number of elements in <math>T</math>.
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==Solution==

Latest revision as of 19:14, 2 May 2025

Problem

Let $S = \{2,7,15,26,....\}$ be the set of all numbers for which the $i^{th}$ element in $S$ is the sum of the $i^{th}$ triangular number and the $i^{th}$ positive perfect square. Let $T$ be the set which contains all unique remainders when the elements in $S$ are divided by $2022$. Find the number of elements in $T$.

Solution

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