April 5th, 2014, 10:50 PM  #1 
Senior Member Joined: Nov 2013 Posts: 434 Thanks: 8  divid
Prove that ( 14578 )^3 × ( 14575 )^3 divides by 3. Last edited by skipjack; April 6th, 2014 at 05:28 AM. 
April 6th, 2014, 12:14 AM  #2 
Senior Member Joined: Apr 2013 Posts: 425 Thanks: 24  If you are talking about $\displaystyle 14578^3 \cdot 14575^3$,then it is not true! What is the condition that the number to be divided by 3?
Last edited by skipjack; April 6th, 2014 at 05:31 AM. 
April 6th, 2014, 05:37 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,098 Thanks: 1905 
I assume that 14578³  14575³ was intended. As the terms have the same digital root, this expression is divisible by 9.
