• Support PF! Buy your school textbooks, materials and every day products Here!

Prime Factorization (Arithmetic)

  • Thread starter cheiney
  • Start date
  • #1
11
0

Homework Statement



Assume n = p_1*p_2*p_3*...*p_r = q_1*q_2*q_3*...*q_s, where the p's and q's are primes. We can assume that none of the p's are equal to any of the q's. Why?

Homework Equations





The Attempt at a Solution



I am completely stuck on this. My understanding of the Fundamental Theorem of Arithmetic is that each number n[itex]\geq[/itex]2 has a unique prime factorization. So how could we possibly assume that the p's aren't equal to the q's?
 

Answers and Replies

  • #2
Office_Shredder
Staff Emeritus
Science Advisor
Gold Member
3,750
99
Is this literally the statement of your homework question?
 
  • #3
phyzguy
Science Advisor
4,395
1,369
I'm with you. The question doesn't make any sense to me either.
 
  • #4
11
0
Is this literally the statement of your homework question?
Yes. The only 2 approaches I could really think of is that, since they didn't specify that n is greater than or equal to 2, so if all of q_j are negative and if j is an even number, then it would hold up. The other approach would be to describe n as a member of a set with "primes" in the sense that they cannot be divisible by other numbers in the set other than 1 and itself.
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
41,808
933
I would be inclined to say that "prime" implies positive and so the "unique factorization property" says, to the contrary of what this purports, that if p_1*p_2*p_3*...*p_r = q_1*q_2*q_3*...*q_s, then the "p"s and "q"s must be equal.
 

Related Threads on Prime Factorization (Arithmetic)

Replies
4
Views
1K
  • Last Post
Replies
2
Views
757
  • Last Post
Replies
12
Views
6K
  • Last Post
Replies
7
Views
2K
  • Last Post
2
Replies
33
Views
1K
  • Last Post
Replies
6
Views
592
  • Last Post
Replies
2
Views
1K
Replies
3
Views
2K
Replies
7
Views
540
Replies
0
Views
853
Top