# Number theory (Primes)

• Sep 8th 2009, 04:59 PM
manusform
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
• Sep 8th 2009, 11:23 PM
CaptainBlack
Quote:

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 \$\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