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Math: Number Theory

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Re: Math: Number Theory [#permalink] New post 27 Feb 2011, 09:04
Any nonzero natural number n can be factored into primes, written as a product of primes or powers of primes. Moreover, this factorization is unique except for a possible reordering of the factors.

Pls give me the example of bold face text because i am not sure what does it exactly means.

Thanks
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Re: Math: Number Theory [#permalink] New post 27 Feb 2011, 09:12
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GMATD11 wrote:
Any nonzero natural number n can be factored into primes, written as a product of primes or powers of primes. Moreover, this factorization is unique except for a possible reordering of the factors.

Pls give me the example of bold face text because i am not sure what does it exactly means.

Thanks


It's called the fundamental theorem of arithmetic (or the unique-prime-factorization theorem) which states that any integer greater than 1 can be written as a unique product of prime numbers.

For example: 60=2^2*3*5 --> 60 can be written as a product of primes (powers of primes) only in this unique way (you can just reorder the multiples and write 3*2^2*5 or 2^2*5*3 ...).
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Re: Math: Number Theory [#permalink] New post 27 Feb 2011, 10:55
If a is a factor of bc, and gcd(a,b)=1, then a is a factor of c.

any particular example.
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Re: Math: Number Theory [#permalink] New post 03 Mar 2011, 04:14
Nice work mates....very informative source to kickkkk start my Prep..... :-D
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Re: Math: Number Theory [#permalink] New post 06 Mar 2011, 04:50
Can someone please explain the following:

1. "Special Cases" section in "Evenly Spaced Integers"

2. Last digit of a power

Thanks.
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Re: Math: Number Theory [#permalink] New post 27 May 2011, 07:21
thank you for the great post. I currently use the GMAT Toolkit app, which I highly recommend, when can I expect this update? In addition, when will the Manhattan GMAT books be updated to the app?

Thanks,
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Re: Math: Number Theory [#permalink] New post 27 May 2011, 08:24
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Hi,

Thanks for your words! 1.6.0 update is available for download. Just get it, go to Store and you can buy any of 10 famous Manhattan GMAT books.

Let me know if you have any questions.

OrenY wrote:
thank you for the great post. I currently use the GMAT Toolkit app, which I highly recommend, when can I expect this update? In addition, when will the Manhattan GMAT books be updated to the app?

Thanks,

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Re: Math: Number Theory [#permalink] New post 17 Jul 2011, 09:18
is this always true?
The product of n consecutive integers is always divisible by n!.
Given consecutive integers: . The product of 3*4*5*6 is 360, which is divisible by 4!=24
.

for example, n=10 and the first number starts at 100000, then this rule doesn't hold.
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Re: Math: Number Theory [#permalink] New post 05 Sep 2011, 00:15
Hi GMAT CLUB,

Thank you for this super book.

I am completely following it for my exam in November.

I am going through the chapter on Number Theory, under heading "Finding the Number of Factors of an Integer".

Please can someone explain how you arrived at the following rule. Is there any proof for it.



For an integer n=a^p*b^q*c^r, where a, b, and c are prime factors of n and p, q, and r are their powers.

The number of factors of n will be expressed by the formula (p+1)(q+1)(r+1).

NOTE: this will include 1 and n itself.

Thank You for your help.
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Re: Math: Number Theory [#permalink] New post 10 Sep 2011, 22:04
This one piece is awesome of all on the math book!
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Re: Math: Number Theory [#permalink] New post 10 Sep 2011, 22:08
gujralam wrote:
Hi GMAT CLUB,

Thank you for this super book.

I am completely following it for my exam in November.

I am going through the chapter on Number Theory, under heading "Finding the Number of Factors of an Integer".

Please can someone explain how you arrived at the following rule. Is there any proof for it.



For an integer n=a^p*b^q*c^r, where a, b, and c are prime factors of n and p, q, and r are their powers.

The number of factors of n will be expressed by the formula (p+1)(q+1)(r+1).

NOTE: this will include 1 and n itself.

Thank You for your help.


Please search for "unique-prime-factorization theorem" on web, you should be able to get what you are looking for!
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Re: Math: Number Theory [#permalink] New post 21 Sep 2011, 01:37
Thanks a lot Bunuel.. truly awesome...
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Re: Math: Number Theory [#permalink] New post 24 Nov 2011, 17:23
This is THE BEST thing anyone has ever posted. THANK YOU SO MUCH.





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Re: Math: Number Theory [#permalink] New post 17 Dec 2011, 07:52
Hi, thanks for the great summary. BTW, do you have a list of questions (just question number) in OG12 + Quant Review 2nd edition to practice, just like the Triangles and Circle section?

Thanks again!
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Re: Math: Number Theory [#permalink] New post 06 Feb 2012, 14:55
Bunnel you simply ROCK!!!! :)
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Re: Math: Number Theory [#permalink] New post 05 Mar 2012, 00:29
Breathtaking post! (Literally!)
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Re: Math: Number Theory [#permalink] New post 06 Mar 2012, 12:00
Bunuel wrote:
NUMBER THEORY

EXPONENTS

Exponents and divisibility:
\(a^n-b^n\) is ALWAYS divisible by \(a-b\).
\(a^n-b^n\) is divisible by \(a+b\) if \(n\) is even.
\(a^n + b^n\) is divisible by \(a+b\) if \(n\) is odd, and not divisible by a+b if n is even.



Hello, Bunuel. Great post!

Do you have an example problem in which this applies. I plugged in numbers to understand the concept I was just curious about the application and seeing this in action. Thanks.
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Re: Math: Number Theory [#permalink] New post 06 Mar 2012, 12:03
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destroyerofgmat wrote:
Bunuel wrote:
NUMBER THEORY

EXPONENTS

Exponents and divisibility:
\(a^n-b^n\) is ALWAYS divisible by \(a-b\).
\(a^n-b^n\) is divisible by \(a+b\) if \(n\) is even.
\(a^n + b^n\) is divisible by \(a+b\) if \(n\) is odd, and not divisible by a+b if n is even.



Hello, Bunuel. Great post!

Do you have an example problem in which this applies. I plugged in numbers to understand the concept I was just curious about the application and seeing this in action. Thanks.


Check this: if-n-is-an-integer-1-is-3-n-2-n-divisible-by-84992.html
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Math: Number Theory [#permalink] New post 06 Mar 2012, 13:32
Bunuel wrote:
destroyerofgmat wrote:
Bunuel wrote:
NUMBER THEORY

EXPONENTS

Exponents and divisibility:
\(a^n-b^n\) is ALWAYS divisible by \(a-b\).
\(a^n-b^n\) is divisible by \(a+b\) if \(n\) is even.
\(a^n + b^n\) is divisible by \(a+b\) if \(n\) is odd, and not divisible by a+b if n is even.



Hello, Bunuel. Great post!

Do you have an example problem in which this applies. I plugged in numbers to understand the concept I was just curious about the application and seeing this in action. Thanks.


Check this:


Awesome! Thanks. That's definitely above my level but good practice no doubt.
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Re: Math: Number Theory [#permalink] New post 17 May 2012, 01:03
Thanks a Tonn for the detailed post and help !!!!!
Re: Math: Number Theory   [#permalink] 17 May 2012, 01:03

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