April 5th, 2014, 09:50 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 04:28 AM. 
April 5th, 2014, 11:14 PM  #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 04:31 AM. 
April 6th, 2014, 04:37 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 19,724 Thanks: 1807 
I assume that 14578³  14575³ was intended. As the terms have the same digital root, this expression is divisible by 9.
