what is mod??

**xXxSANJIxXx** · August 11th 2006, 01:58 AM

im in year 7 so can someone help me with that modulo thing.. i nedd someone to explain it to me.

**Jameson** · August 11th 2006, 06:17 AM

Here's a brief Wikipedia explanation.

http://en.wikipedia.org/wiki/Modular_arithmetic

**ThePerfectHacker** · August 11th 2006, 07:07 AM

Sometimes for basic explanations Wikipedia is not ideal for it is complicated.
---
$a,b,n$ are integers and $n\not = 0$
---
When we write,
$a\equiv b (\mbox{mod } n)$
We mean that $a-b$ is divisible by $n$ .
For example,
$5\equiv 3 (\mbox{mod } 2)$ because, $5-3=2$ which is divisible by two.
For example,
$5\not \equiv 2 (\mbox{mod } 2)$ because $5-2=3$ which is not divisible by 2.

**Soltras** · August 11th 2006, 07:19 AM

You can think of doing modular artithmetic kind of the same way you would, say, figure time on a clock.

In modulo 12, 10+3 = 1
because 10+3=13, of course, but 13 mod 12 = 1 because 13 divided by 12 leaves a remainder of 1.

Similarly, on a clock, 10pm + 3 hours = 1 am, not 13pm.

And then 1:00 + 18 hours = 1:00 + 6 hours = 7:00.
Because 18 mod 12 = 6.

So you've been using modular arithmetic as long as you've been telling time without knowing it was modular arithmetic. That knowledge will hopefully make you more comfortable with using it now in other modulos than 12.

**dan** · August 11th 2006, 07:34 AM

Can’t (a mod b) be defined as the integer remainder of a/b ??....more or less

Dan

**ThePerfectHacker** · August 11th 2006, 07:47 AM

Originally Posted by dan

Can’t (a mod b) be defined as the integer remainder of a/b ??....more or less

Dan

Yes, but that is not the common way to use them. The common way is mention in my other post. That is exactly how they are used in number theory.

**Glaysher** · August 11th 2006, 07:55 AM

Year 7 means 11 years old if he is from England so would probably not be familiar with that notation. However it would not be part of the syllabus either so you never know.

If I'm right he need a different solution to his previous post

**dan** · August 11th 2006, 08:22 AM

ph,
In your post about mod you used what looked like an equals sign but it had three lines. I have never seen that before ...what does it mean?
Dan

**Quick** · August 11th 2006, 08:27 AM

Originally Posted by dan

ph,
In your post about mod you used what looked like an equals sign but it had three lines. I have never seen that before ...what does it mean?
Dan

it is an equivilant I posted this question before here .

**Rebesques** · August 11th 2006, 08:31 AM

It's just notation, so long as you can just solve problems and not mind!

(Actually, $a\equiv b \ {\rm mod}n$ means a and b are members of the "equivalence relation" defined by: "having the same residue when divided by n").

**dan** · August 11th 2006, 09:20 AM

k thanks
dan

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