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What is the smallest positive integer \(n\) such that \(531n \equiv 1067n \pmod{24}?\)

 
 Oct 10, 2021
 #1
avatar+114826 
+2

 

 

\(531n \equiv 1067n \pmod{24}\\ 24*22n+3n \equiv 24*44n+11n \pmod{24}\\ 0+3n \equiv 0+11n \pmod{24}\\ 3n \equiv 11n \pmod{24}\\ 8n \equiv 0 \pmod{24}\\ n=0,3,6,9,etc\\ \text{The smallest positive n is 3}\)

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 Oct 11, 2021
 #2
avatar+90 
+1

Thank you Melody! It really helped :)

 
 Oct 11, 2021

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