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Math Help - Number theory (Primes)

  1. #1
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    Number theory (Primes)

    pls help me with this problem. i tried to solve but it i can't get it.

    *Determine whether the following assertions are true or false. if true, prove the result, and if false, give a counter example

    1. If a^3/c^3 then a/c
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by manusform View Post
    pls help me with this problem. i tried to solve but it i can't get it.

    *Determine whether the following assertions are true or false. if true, prove the result, and if false, give a counter example

    1. If a^3/c^3 then a/c
    We would normally write this a^3|c^3 which reads a cubed divides c cubed (I will aslo assume for simplicity that a and c are both natural numbers).

    This is true, to prove it consider the prime decompositions of a and c. It can also be done by contradiction - supose that a^3|c^3, but a \not| c.

    CB
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