Math Is Fun Forum
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#1 2014-09-05 15:52:16
Modular Arithmetic
Evaluate: 7^7^7 mod 13
'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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#2 2014-09-05 20:14:34
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modular Arithmetic
When p is prime and a is not divisible by p:
By Fermats little theorem:
so we are left with
so
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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#3 2014-09-05 22:03:00
Re: Modular Arithmetic
I can't believe this!
From where did you get 12?
'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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#4 2014-09-06 01:56:45
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modular Arithmetic
To make the formula work you need p - 1.
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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#5 2014-09-06 02:11:22
Re: Modular Arithmetic
What is 68628?
'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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#6 2014-09-06 02:12:41
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modular Arithmetic
12 * 68628 + 7 = 7^7
I can't believe this!
There are other ways to do this that do not invoke that formula.
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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#7 2014-09-06 04:45:22
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Modular Arithmetic
Hi,
Can also be computed by using binary exponentiation.
In python,
pow(7, 7**7, 13) # = 6"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#8 2014-09-06 04:47:13
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modular Arithmetic
Hello gAr, Howdy!
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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#9 2014-09-06 14:53:04
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Modular Arithmetic
Hello!
Hope you all are doing well.
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#10 2014-09-06 14:56:19
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modular Arithmetic
Howdy;
Just the same which I suppose is good. What have you been doing?
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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#11 2014-09-06 18:24:14
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Modular Arithmetic
Hi,
That's good then.
I have been teaching and learning!
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#12 2014-09-06 18:27:27
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modular Arithmetic
Teaching? Who are you teaching?
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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#13 2014-09-06 18:38:09
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Modular Arithmetic
Teaching students as a part of my job.
Felt like company jobs are rubbish.
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#14 2014-09-06 18:41:00
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modular Arithmetic
Oh very good! I am glad to hear that. They have a good teacher.
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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#15 2014-09-06 18:46:23
Re: Modular Arithmetic
I am sorry, that was not the original question.
'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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#16 2014-09-06 18:47:18
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modular Arithmetic
What is the question?
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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#17 2014-09-06 18:51:07
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Modular Arithmetic
Thanks!
Don't know whether I'll be good or not, giving it a try anyway.
You may remember me telling earlier that I did not want a teaching job, but now here I am!
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#18 2014-09-06 18:56:57
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modular Arithmetic
gAr meet my friend Agnishom. Agnishom, meet gAr! gAr does EM.
I have to go now and cook dinner see you all later.
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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#19 2014-09-06 19:07:49
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Modular Arithmetic
Okay, enjoy your dinner.
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#20 2014-09-06 21:16:20
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modular Arithmetic
Hi gAr;
Sorry about that. He came in at an odd time. I think you will find teaching can be rewarding personally.
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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#21 2014-09-07 03:12:41
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Modular Arithmetic
Hi,
No problem.
I too hope so, all I need is time to chew on the bits and numbers!
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#22 2014-09-07 03:30:21
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modular Arithmetic
Will you throw some experimental math at them once in a while?
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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#23 2014-09-07 03:45:20
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Modular Arithmetic
First trying to make them adept at programming.
Or else, they will get both the code and math wrong!
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#24 2014-09-07 03:50:01
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Modular Arithmetic
How old are they?
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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#25 2014-09-07 03:52:17
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Modular Arithmetic
About 18+
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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