how would you simplify this?

27=45(mod 8)

so that its' residue is lesser than it's divisor (mod 8)

Question

how would you simplify this?

27=45(mod 8) 

so that its' residue is lesser than it's divisor (mod 8)

kinggeorge · Answer

I'm confused... Maybe I'm just not understanding what a residue is, but $$27 \neq 45 \quad (\text{\mod} \:\:\:8)$$Rather, $27 = 3 \quad (\text{mod} \:\:\: 8) $  and  $45 = 5 \quad (\text{mod} \:\:\: 8) $

anonymous · Answer

tha residue is 45, the other name for the residue is remainder. .  

i've been looking on the internet since then, but i haven't found any way on how to simplify such.

anonymous · Answer

excuse me, it's -27

kinggeorge · Answer

That makes more sense.

anonymous · Answer

can you help me?

kinggeorge · Answer

Well, the easiest way to simplify this problem, is to simply take$${45 \over 8} = 5.625$$so you know the quotient is 5. Then$$45- 8*5 = 45-40 = 5$$so the residue/remainder would be 5. A similar process can be used for -27. In this case, both have residue of 5.

anonymous · Answer

you mean. .

-27-40=45-40(mod8)
would result to              -67=5(mod 8)?

kinggeorge · Answer

That is correct.

anonymous · Answer

AHH, THANKS. .

kinggeorge · Answer

your welcome.

Any other quick modular arithmetic questions?

anonymous · Answer

nope, at this moment. .  perhaps, in other times. .  lol thanks again. .