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#1 2008-11-04 09:10:20
- GemmaJ1988
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- Registered: 2008-10-08
- Posts: 39
primes
i have the following question
write
does anyone know what this is actually asking me to do.
please help
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#2 2008-11-04 18:25:36
- Ricky
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- Registered: 2005-12-04
- Posts: 3,791
Re: primes
The "question" is asking you to prove that given any natural number n, we may write n as a product of distinct primes.
90 = 2*45 = 2*(3*15) = 2*(3*(3*5))
Above is the basic method used to prove it, though a nicer (but slightly less obvious) way exists.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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#3 2008-11-05 02:16:19
- GemmaJ1988
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- Registered: 2008-10-08
- Posts: 39
Re: primes
is n not already expressed as its product of distinct primes then?
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#4 2008-11-05 04:29:17
- Ricky
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- Registered: 2005-12-04
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Re: primes
You need to prove that n _can be_ expressed as a product of primes.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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#5 2008-11-05 11:15:28
- GemmaJ1988
- Member
- Registered: 2008-10-08
- Posts: 39
Re: primes
so i've looked up the fundamental theorem of arithmetic and ive tried to apply this to n
i got
if we set
does this seem remotely along the right lines?
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#6 2008-11-05 11:27:36
- Ricky
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- Registered: 2005-12-04
- Posts: 3,791
Re: primes
No. The Fundamental Theorem of Arithmetic is specifically what you are trying to prove.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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