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Multiplying any integer with any prime

  1. Aug 9, 2013 #1

    ull

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    PS. I dont speak or write english very well. I´m doing my best. Is it still ok to post questions?

    a = any integer
    b = any prime number

    a * b = c

    Is there a proof that "c" isnt made up by any other prime factors than the prime factors that make up "a" (except for "b")?
     
  2. jcsd
  3. Aug 9, 2013 #2
    It's a result of the fundamental theorem of arithmetic. :wink:
     
  4. Aug 10, 2013 #3
    Sinse a prime number can only be divided by 1 and itself, no two numbers can ever equal a prime number. I don't know what the proof is called though. I think the OP wants to know the name of the actual law/proof.
     
  5. Aug 10, 2013 #4
    As Mandelbroth said, the proof is the fundamental theorem of arithmetic, from which the OP's desired result follows immediately.
     
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