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#76 2014-12-05 02:27:36

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,135

Re: Find the unit digit of the number n

(8 mod 7 x 8 mod 7... )


Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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#77 2014-12-05 02:28:48

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the unit digit of the number n

That is very good. What does 8 mod 7 do?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#78 2014-12-05 02:30:41

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,135

Re: Find the unit digit of the number n

8 mod 7 get you the Reminder of 8 / 7 which is 1?


Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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#79 2014-12-05 02:35:54

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the unit digit of the number n

That is very good.

Now what do we get here:

(8 mod 7) (8 mod 7)...


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#80 2014-12-05 02:36:33

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,135

Re: Find the unit digit of the number n

1


Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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#81 2014-12-05 02:37:41

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the unit digit of the number n

Yes, it is 1 x 1 x 1 x 1 ...

So the answer is?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#82 2014-12-05 02:38:48

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,135

Re: Find the unit digit of the number n

The answer is 1


Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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#83 2014-12-05 02:42:13

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the unit digit of the number n

So

This is written in a special way.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#84 2014-12-05 02:42:52

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,135

Re: Find the unit digit of the number n

What else is on the learning list?


Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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#85 2014-12-05 02:48:36

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the unit digit of the number n

You should see the notation and get used to it.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#86 2014-12-05 02:50:04

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,135

Re: Find the unit digit of the number n

I will try and look around online, thanks for today.
I think I want to get my eye shut now, night.
Happy shopping!


Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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#87 2014-12-05 02:52:59

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the unit digit of the number n

Get some rest, we will do more tomorrow if you want.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#88 2014-12-05 02:54:10

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,135

Re: Find the unit digit of the number n

You get some rest too. But do wake up tongue


Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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#89 2014-12-05 03:02:37

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the unit digit of the number n

Not likely, I will sleep, I have a busy day ahead.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#90 2014-12-05 04:33:44

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

Re: Find the unit digit of the number n

Chris, do you have mathematica?

Did you know that you can use this command in mathematica to do this problem:

Mod[8^2014,7]

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#91 2014-12-05 04:42:34

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the unit digit of the number n

Yes, I will soon wean him into the ways of the real m.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#92 2014-12-05 04:50:11

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

Re: Find the unit digit of the number n

chooipian wrote:

What else is on my learning list?

bobbym was correct about the learning part.

You just need to see the congruences as equations on which you can do just about anything on both sides.

There isn't basically many things to learn here. On the other hand, there is a 70% chance that every number theory olympiad paper has a question that says 'Find the remainder when ... '. There are many techniques here that you can master only by trying to solve problems.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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