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Fundamental Theorem of Arithmetic Problem 
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#1
Aug2009, 12:31 PM

P: 85

Problem number 4 on the image has me stumped. I understand the problem (obviously not enough) and what its saying, I'm just having trouble putting it into a proof. Can i get a hint to get me started? Thanks
http://img40.imageshack.us/i/asdasdjql.jpg/ 


#2
Aug2009, 12:44 PM

P: 57

I think you should pay attention to the fact t1 , t2, etc . are greater than OR EQUAL TO zero.
This should solve your purpose. 


#3
Aug2009, 01:01 PM

Sci Advisor
HW Helper
P: 3,684

Fisicks, I don't know what problem you have. The basic idea is simple: sort the q_i and s_i in order and put them into one big list. When a number comes from both lists, add the exponents; otherwise take the exponent from where it came (e_i or f_i). Example: (3^2 * 2^1) * (7^2 * 2^2 * 3^3) = (2^1 * 3^2) * (2^2 * 3^3 * 7^2) = 2^(1+2) * 3^(2+3) * 7^2 = 2^3 * 3^5 * 7^2 


#4
Aug2009, 05:13 PM

P: 85

Fundamental Theorem of Arithmetic Problem
greathouse why are you multiplying exponents, its just representing a and b to have the same bases of primes, and what i need help with is the proof part, not the what is the problem saying part.



#5
Aug2109, 12:13 AM

Sci Advisor
HW Helper
P: 3,684

Sorry, misread the problem. Your problem is easier  just ignore the part about adding, and take missing primes' exponents to be 0.



#6
Aug2109, 12:10 PM

P: 85

yeah i get that part!!! i need to know how you would write a formal proof to show that, cause thats what the problem is asking.



#7
Aug2109, 01:25 PM

Sci Advisor
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P: 3,684

Without knowing the requirements for your "formal" proof I couldn't possibly start. I don't imagine you mean what I mean when I say 'formal'.



#8
Aug2109, 01:49 PM

P: 85

i don't know what more you want, the question is posted right up there in that link lol. all i want to know is how to answer that question.



#9
Aug2109, 05:19 PM

P: 894




#10
Aug2109, 07:06 PM

P: 993




#11
Aug2109, 10:04 PM

P: 894




#12
Aug2209, 12:18 AM

P: 993

Problem 3 isn't enough, it just "collects" equal primes into single powers. In problem 4 you have to "split" the product by introducing powers of 0. A proof along the lines suggested by CRGreathouse is what the problem's asking for, I think.
You can use problem 3 to say that a*b has a unique factorization, but you won't be able to say that a can be expressed with the prime factors of b directly, which is required for problem 3 to apply. 


#13
Aug2209, 07:57 AM

P: 894




#14
Aug2309, 04:52 PM

P: 993

Not having seen the rest of the book, I don't know how problem 3 really relates to problem 4. But the fact is that to use the result of 3, you need to have the prime factorization. However, 1 isn't a prime, so you can't just use the fact that p^0=1.



#15
Aug2309, 09:49 PM

P: 894




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