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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- Sep 8th 2009, 04:59 PMmanusformNumber 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 - Sep 8th 2009, 11:23 PMCaptainBlack
We would normally write this $\displaystyle a^3|c^3$ which reads $\displaystyle a$ cubed divides $\displaystyle c$ cubed (I will aslo assume for simplicity that $\displaystyle a$ and $\displaystyle c$ are both natural numbers).

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

CB