1. ## 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

2. Originally Posted by manusform
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