My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
September 15th, 2009, 05:40 AM   #1
Newbie
 
Joined: Aug 2009

Posts: 12
Thanks: 0

Algebra...

plis help me to solve this questions......
1. Find the remainder when 7^2005 divide by 5.....
2. The sum of a whole number , N and 2005 can be divided respectively by 11 and 9..Find the lowest value of N.
plis help me to solve this questions....
hannif razak is offline  
 
September 15th, 2009, 07:37 AM   #2
Senior Member
 
Joined: Jan 2009
From: Japan

Posts: 192
Thanks: 0

Re: Algebra...

1. Try working out the first few of these until you spot a pattern of repetition. You need only worry about the last digit (why?) for the multiplications. Then figure out where 2005 falls in that pattern.
cmusick is offline  
September 15th, 2009, 04:16 PM   #3
Newbie
 
Joined: Aug 2009

Posts: 12
Thanks: 0

Re: Algebra...

urm.....i dont understand.....
hannif razak is offline  
September 15th, 2009, 05:21 PM   #4
Senior Member
 
Joined: Jan 2009
From: Japan

Posts: 192
Thanks: 0

Re: Algebra...

List them out:
Last digit of 7 = 7
Last digit of 7 * 7 =
Last digit of (7 * 7) * 7 =
Last digit of (7^3) * 7 =
Last digit of (7^4) * 7 =
Last digit of (7^5) * 7 =
etc.

You'll see a pattern to it. If the pattern is, for example (and this is NOT the pattern) 1, 2, 3, 1, 2, 3, 1, 2, 3, ...
You can use division to figure out where the 2005th power of 7 would appear on the list. You only need the last digit because the remainder when dividing by 5 only depends on the last digit of a number.
cmusick is offline  
September 16th, 2009, 07:31 AM   #5
Global Moderator
 
Joined: Dec 2006

Posts: 20,484
Thanks: 2041

1. Or use the fact that 7^2005 = 7((5(480) + 1)^501).
2. Is this worded correctly? N can be 11, which is very obviously its lowest possible positive value, but if negative values are allowed N can be as low as you like. In any case, it's unclear what "respectively" means in this context (for N = 11 to work, a particular interpretation is needed).
skipjack is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
algebra



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Algebra HELP PlzzHelp Algebra 7 February 5th, 2013 01:20 PM
Algebra solver in several algebra equations malylo Algebra 2 November 10th, 2011 12:33 PM
Algebra mathswizard Algebra 7 October 5th, 2011 03:32 AM
algebra Abigail_01_92 Algebra 7 November 26th, 2009 09:35 AM
Algebra: Unanswered Questions in My Algebra Textbook polydorus Algebra 10 February 21st, 2009 10:20 AM





Copyright © 2019 My Math Forum. All rights reserved.