bellabasketball4626 bellabasketball4626

05-08-2017
Mathematics

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When a positive integer k is divided by 6, the remainder is 1. what is the remainder when 5k is divided by 3?

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LammettHash LammettHash

06-08-2017

[tex]k\equiv1\mod6\implies k=6n+1[/tex] for some integer [tex]n[/tex].

[tex]5k=5(6n+1)=30n+5[/tex]
[tex]\implies5k\equiv30n+5\equiv3(10n)+5\equiv5\equiv2\mod3[/tex]

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