My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum


Thanks Tree6Thanks
  • 2 Post By Micrm@ss
  • 1 Post By Micrm@ss
  • 1 Post By skipjack
  • 1 Post By 1010010010
  • 1 Post By JeffM1
Reply
 
LinkBack Thread Tools Display Modes
July 16th, 2017, 03:22 AM   #1
Newbie
 
Joined: Apr 2017
From: Bhadohi, U.P., India

Posts: 18
Thanks: 0

find the number

find the number
Attached Images
File Type: jpg IMG_20170716_165007.jpg (18.3 KB, 25 views)
Shariq Faraz is offline  
 
July 16th, 2017, 03:27 AM   #2
Senior Member
 
Joined: Oct 2009

Posts: 141
Thanks: 59

Write $n^5 + 5 = (n^5 - 5^5) + (5^5 + 5)$.
Thanks from JeffM1 and Shariq Faraz
Micrm@ss is offline  
July 16th, 2017, 10:38 AM   #3
Newbie
 
Joined: Apr 2017
From: Bhadohi, U.P., India

Posts: 18
Thanks: 0

please explain further
Shariq Faraz is offline  
July 16th, 2017, 12:28 PM   #4
Senior Member
 
Joined: Oct 2009

Posts: 141
Thanks: 59

Can you show that $n+5$ always divides $n^5 + 5^5$ by factorizing the latter?

Then what does that mean for $n^5 + 5 = (n^5 + 5^5) - (5^5 + 5)$?
Thanks from Shariq Faraz
Micrm@ss is offline  
July 16th, 2017, 01:07 PM   #5
Global Moderator
 
Joined: Dec 2006

Posts: 17,919
Thanks: 1386

Getting the signs right would help. One can use the factor theorem or the remainder theorem.
Thanks from Shariq Faraz
skipjack is offline  
July 16th, 2017, 04:55 PM   #6
Newbie
 
Joined: Jul 2017
From: Asia

Posts: 2
Thanks: 1

Untitled.jpg
Thanks from Shariq Faraz

Last edited by skipjack; July 16th, 2017 at 06:07 PM.
1010010010 is offline  
July 16th, 2017, 06:52 PM   #7
Senior Member
 
Joined: May 2016
From: USA

Posts: 785
Thanks: 312

Quote:
Originally Posted by Shariq Faraz View Post
please explain further
$\dfrac{n^5 + 5}{n + 5} =$

$n^4 - 5n^3 + 25n^2 - 125n + 625 - \dfrac{3120}{n + 5}.$

Simple division.

$n \in \mathbb Z \implies x = n^4 - 5n^3 + 25n^2 - 125n + 625 \in \mathbb Z.$

$n > 3115 \implies n + 5 > 3120 > 0 \implies 1 > \dfrac{3120}{n + 5} > 0 \implies$

$x + 1 > x + \dfrac{3120}{n + 5} > x \implies x + \dfrac{3120}{n + 5} \not \in \mathbb Z$

$\therefore n \le 3115.$
Thanks from Shariq Faraz
JeffM1 is offline  
Reply

  My Math Forum > College Math Forum > Number Theory

Tags
find, number



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Find out the least number burgess Algebra 10 July 2nd, 2014 06:01 AM
how to find number of factors of a number ? MATHEMATICIAN Number Theory 15 August 26th, 2013 10:16 PM
FIND THE NUMBER X , Y and Z. please help me pappi_1984 Calculus 1 December 24th, 2012 02:06 AM
find unique n number combination in total n number jsonliu Algebra 3 May 18th, 2010 05:01 PM
Find out the odd number Atul Real Analysis 0 December 31st, 1969 04:00 PM





Copyright © 2017 My Math Forum. All rights reserved.