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Difference between revisions of "2022 SSMO Relay Round 5 Problems/Problem 2"

(Created page with "==Problem== Let <math>T=</math> TNYWR, and let <math>S=\{a_1,a_2,\dots,a_{2022}\}</math> be a sequence of 2022 positive integers such that <math>a_1\le a_2\le \cdots \le a_{20...")
 
 
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==Problem==
 
==Problem==
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Let <math>T=</math> TNYWR, and let <math>S=\{a_1,a_2,\dots,a_{2022}\}</math> be a sequence of 2022 positive integers such that <math>a_1\le a_2\le \cdots \le a_{2022}</math> and <math>\text{lcm}(a_1,a_2,\dots,a_{2022})=70T</math>. Also, <math>\text{gcd}(a_i,a_j)=1</math> for all <math>1\le i<j\le2022</math>. Find the number of possible sequences <math>S</math>.
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Let <math>T=TNYWR</math>, and let <math>S=\{a_1,a_2,\dots,a_{2022}\}</math> be a sequence of 2022 positive integers such that <math>a_1\le a_2\le \cdots \le a_{2022}</math> and <math>\text{lcm}(a_1,a_2,\dots,a_{2022})=70T</math>. Also, <math>\text{gcd}(a_i,a_j)=1</math> for all <math>1\le i<j\le2022</math>. Find the number of possible sequences <math>S</math>.
  
 
==Solution==
 
==Solution==

Latest revision as of 19:24, 2 May 2025

Problem

Let $T=TNYWR$, and let $S=\{a_1,a_2,\dots,a_{2022}\}$ be a sequence of 2022 positive integers such that $a_1\le a_2\le \cdots \le a_{2022}$ and $\text{lcm}(a_1,a_2,\dots,a_{2022})=70T$. Also, $\text{gcd}(a_i,a_j)=1$ for all $1\le i<j\le2022$. Find the number of possible sequences $S$.

Solution

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