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Prove by complete induction that any natural number $n\ge2$ is equal to a product of prime numbers.

almagest
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  • Do you mean that "Every number can be written as a product of prime , which is unique apart from the order" ? – The Demonix _ Hermit Jan 08 '20 at 16:57
  • Induction has to go downward. A number $n$ either has factors less than itself but more than 1 or it doesn't. If it doesn't than it is a prime number. If it does then those factors are smaller and you use the same argument on them. And $n$ is finite inductively we "go down" and eventually must end with numbers that can't go further. Those number have no factors other than themselves or 1 and thus are prime and $n$ is the product of them. – fleablood Jan 08 '20 at 17:04
  • Prove ......... – none Jan 08 '20 at 17:10

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