Quick question about modulus:
-8 (modulus equal operator) |blank space| (mod 7)

is it -1?

Question

Quick question about modulus:
-8 (modulus equal operator) |blank space| (mod 7)

is it -1?

triciaal · Answer

can you restate the question? this is not clear

zyberg · Answer

-8 (modulus equal operator) |blank space| (mod 7)

ganeshie8 · Answer

Hi

ganeshie8 · Answer

The question is asking you to find the remainder when -8 is divided by 7

Still remember long division ?

zyberg · Answer

Hi, @ganeshie8 ;) This time just flying around modular arithmetics, trying to get basics really good (and being amazed about some neat problems and how easy it is to solve everything with modulus).

zyberg · Answer

Yeah, I think that the answer would be -1, is it right?

ganeshie8 · Answer

-1 is one remainder
But it is not the least nonnegative remainder

zyberg · Answer

So, the answer is 6?

zyberg · Answer

(seems so weird that dividing -8 could give off 6 as a remainder, but I guess it has some logic behind itself)

ganeshie8 · Answer

Awesome! 
modular arithmetic and congruences are really useful if you're preparing for Olympiads
They simplify many divisibility proofs

ganeshie8 · Answer

Let me ask you a question

zyberg · Answer

Yes? ;)

ganeshie8 · Answer

Suppose you owe me 8 cookies

ganeshie8 · Answer

Today morning you gave me 14 cookies.

How many cookies you owe me now ?

zyberg · Answer

0 ;) 
(or -6, if you say :D)

ganeshie8 · Answer

Looks that is a poor example ... scratch that haha

ganeshie8 · Answer

Keep this one thing in mind while you study modular arithmetic :

ganeshie8 · Answer

when you divide a number by another number, the remainder is NOT unique.

zyberg · Answer

What do you mean by that?

ganeshie8 · Answer

What's the remainder when you divide 5 by 3 ?

zyberg · Answer

2 and -1

ganeshie8 · Answer

Are those the only remainders possible ?

zyberg · Answer

Do you mean that from irrational numbers we could do something as fancy as 5/3 = 1.6 with a remainder of 0.0(6)?

ganeshie8 · Answer

The remainders when 5 is divided by 3  are all the numbers of form 3k + 2

ganeshie8 · Answer

Notice that 2 is the least nonnegative remainder herw

zyberg · Answer

Oh! I got what you mean now!

ganeshie8 · Answer

I'll let you keep going with your textbook or whatever. Enjoy ..

zyberg · Answer

Thank you very much, @ganeshie8 :)

ganeshie8 · Answer

Np  :)