powerpuffhere powerpuffhere
  • 01-06-2020
  • Mathematics
contestada

Suppose b is any integer. If b mod 12 = 5, then 7b mod 12

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LammettHash
LammettHash LammettHash
  • 01-06-2020

The result follows directly from properties of modular arithmetic:

[tex]b\equiv5\pmod{12}\implies 7b\equiv35\equiv-1\equiv\boxed{11}\pmod{12}[/tex]

That is,

[tex]b\equiv5\pmod{12}[/tex]

means we can write [tex]b=12n+5[/tex] for some integer [tex]n[/tex]. Then

[tex]7b=7(12n+5)=12(7n)+35[/tex]

and taken mod 12, the first term goes away, so

[tex]7b\equiv35\pmod{12}[/tex]

etc

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