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## Modular arithmetic

i might be making it up, but i am confused.

can we say:

$$x\equiv$$2 (mod k)
$$x\equiv$$2 (mod m)
hence
$$x\equiv$$2 (mod km) by km i mean k multiplied by m.

if not, what is the result? or can it be found?

 Blog Entries: 1 Recognitions: Homework Help No. k=4 m=8 x=10 x=2(mod 4) and x=2(mod 8) but x=10(mod 32) In general, if you have something mod m and something mod k, and want to discuss what happens mod mk, then you need a condition on m and k being coprime, or something similar.
 Blog Entries: 1 thank you for your answer. i think i found sth: say (k,m) = 1 x=a (mod k) x=a (mod m) x=kt+a and x=my+a kt=my t=mb y=kb then x=kmb+a x-a=kmb x-a=0 (mod km) x=a (mod km) it is valid, isnt it? any counterexamples?

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Homework Help

## Modular arithmetic

That looks pretty good to me
 Blog Entries: 1 :) then my problem is solved. now i should get back to work.
 Recognitions: Gold Member Science Advisor Staff Emeritus Yeah, I hate when that happens!