Math Is Fun Forum / Modulo

Harold · 2012-10-12 19:51:12

Can you help me with these two problem
-23 mod 5
23 mod -5
and,could you please explain modulo with nagetive number?

bobbym · 2012-10-12 20:20:23

Hi;

If you use this formula you will have no problems with modulo.

Where

is called the floor function and is evaluated like this:

and

it always rounds down to the smallest integer.

Let's do the first one:

-23 mod 5

You are looking for r, the remainder. a = -23 and m is the modulo, in this case 5.

Now

So -23 mod 5 is 2.

You try the second one. Let me know what you get.

Harold · 2012-10-12 21:56:51

It is -2,is nagetive number allowed as result?

bobbym · 2012-10-12 22:21:10

Hi;

Yes, unless you are told it must be positive.

Harold · 2012-10-12 22:30:24

Thank you^infinity

bobbym · 2012-10-12 23:07:52

Hi;

You are welcome. Were you able to do the second problem?

bob bundy · 2012-10-12 23:50:15

hi bobbym,

Yes he has (in post 3). He got -2

The definition for modulo regarding + or - is uncertain. See http://en.wikipedia.org/wiki/Modulo_operation

Harold ought to check how it has been defined by his teacher.

Bob

bobbym · 2012-10-13 00:10:13

Hi;

Yes he has (in post 3). He got -2

I see that now. He got the right answer too.

Sometimes it has to be the same sign as the divisor. I gave him the one that gets the same answers as Wolfram would.

Unfortunately he skeddadled right after he solved it. I wanted to go a little deeper.

Harold · 2012-10-13 02:21:18

Guys,I have another problem,my brother says that 23 mod -5 will be 3 as Euclidean division states a=bq+r and the division will be 23=(-5)*(-4)+3.

bob bundy · 2012-10-13 03:15:27

hi Harold,

In effect, that was my point in post 7.

The following are all equivalent mod 5

-12, -7, -2, 3, 8, 13, 18 ......

Basically just add 5.

If you follow my link to Wiki you will see that two definitions are possible and there are even more variations amongst computer languages.

Your brother is right using the 'Euclidean division' definition ... under this no negatives are allowed.

Which is why I think you need to check with your teacher / tutor and see what definition is required.

Bob

Harold · 2012-10-13 19:30:24

I am sorry to bug again but after you gave me the formula,i experimented a little and solution to -23 mod -5 results -43,is it correct

bobbym · 2012-10-13 20:24:25

Hi;

I am getting -3 as the answer. Can I see what you have done?

bob bundy · 2012-10-13 20:47:16

Looks like -23 - 20 = -43 rather than -23 + 20 = -3

There are a lot of minus signs to take account of. Easy to slip up on that.

Bob

bobbym · 2012-10-13 21:00:24

Hi;

I am getting

Harold · 2012-10-13 22:43:55

You're right,i missed a minus sign,thank you a lot,you guys taught me a lot of things today.

bobbym · 2012-10-13 22:49:15

Hi Harold;

Use a calculator to at least check.

bob bundy · 2012-10-14 18:51:07

Am I right about this:

The formula should always give a value x, so that -m < x < m (assuming m is positive ... reverse the signs otherwise)

Bob

bobbym · 2012-10-14 20:37:55

Hi bob;

If you did that what do you get for -65 mod -17?

bob bundy · 2012-10-14 20:57:00

Good morning bobbym

Bob

bobbym · 2012-10-14 21:02:32

Hi Bob;

Good Morning.

That is what I am getting too.

bob bundy · 2012-10-14 21:08:00

My point was that Harold can eliminate obvious errors such as -43 on the grounds that it is out of range.

Bob

bobbym · 2012-10-14 21:11:05

Hi;

Yes, it is an obvious error, the answer can never exceed m. In either direction.

Login

Ads

Menu

#1 2012-10-12 19:51:12

Modulo

#2 2012-10-12 20:20:23

Re: Modulo

#3 2012-10-12 21:56:51

Re: Modulo

#4 2012-10-12 22:21:10

Re: Modulo

#5 2012-10-12 22:30:24

Re: Modulo

#6 2012-10-12 23:07:52

Re: Modulo

#7 2012-10-12 23:50:15

Re: Modulo

#8 2012-10-13 00:10:13

Re: Modulo

#9 2012-10-13 02:21:18

Re: Modulo

#10 2012-10-13 03:15:27

Re: Modulo

#11 2012-10-13 19:30:24

Re: Modulo

#12 2012-10-13 20:24:25

Re: Modulo

#13 2012-10-13 20:47:16

Re: Modulo

#14 2012-10-13 21:00:24

Re: Modulo

#15 2012-10-13 22:43:55

Re: Modulo

#16 2012-10-13 22:49:15

Re: Modulo

#17 2012-10-14 18:51:07

Re: Modulo

#18 2012-10-14 20:37:55

Re: Modulo

#19 2012-10-14 20:57:00

Re: Modulo

#20 2012-10-14 21:02:32

Re: Modulo

#21 2012-10-14 21:08:00

Re: Modulo

#22 2012-10-14 21:11:05

Re: Modulo

Board footer