My Math Forum  

Go Back   My Math Forum > High School Math Forum > Pre-Calculus

Pre-Calculus Pre-Calculus Math Forum


Thanks Tree2Thanks
  • 1 Post By tahirimanov19
  • 1 Post By skipjack
Reply
 
LinkBack Thread Tools Display Modes
October 6th, 2019, 03:57 AM   #1
Senior Member
 
Joined: Dec 2015
From: somewhere

Posts: 734
Thanks: 98

Solve for integers

$\displaystyle 2a+3b =5ab$. Find all pairs (a,b) .
idontknow is offline  
 
October 6th, 2019, 05:35 AM   #2
Senior Member
 
Joined: Mar 2015
From: Universe 2.71828i3.14159

Posts: 132
Thanks: 49

Math Focus: Area of Circle
Quote:
Originally Posted by idontknow View Post
$\displaystyle 2a+3b =5ab$. Find all pairs (a,b) .
$a= \dfrac{3b}{5b-2}$

For an integer $a$, $|3b| \ge |5b-2|$, also $|3b| = |5b-2| \times k, \; k \in \mathbb{Z}$

rest is easy....
Thanks from idontknow

Last edited by tahirimanov19; October 6th, 2019 at 05:37 AM.
tahirimanov19 is offline  
October 6th, 2019, 10:02 PM   #3
Global Moderator
 
Joined: Dec 2006

Posts: 21,035
Thanks: 2271

Quote:
Originally Posted by tahirimanov19 View Post
For an integer $a$, $|3b| \ge |5b-2|$
That's incorrect.

As $\displaystyle 0 < \frac{3b}{5b- 2} < 1$ for $b < 0$ or $b > 1$, $b = 0$ (so $a = 0$) or $b = 1$ (so $a = 1$).
Thanks from idontknow
skipjack is offline  
October 6th, 2019, 11:26 PM   #4
Senior Member
 
Joined: Dec 2015
From: somewhere

Posts: 734
Thanks: 98

Just posted the equation to know when $\displaystyle 5b-2 $ can divide $\displaystyle 3b$, which happens only when $\displaystyle b=1$.
from now the value of $\displaystyle a$ is known.

Also we can set 3b=0 , since it can be divided by all integers except 0.
idontknow is offline  
Reply

  My Math Forum > High School Math Forum > Pre-Calculus

Tags
integers, solve



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Solve for integers idontknow Elementary Math 1 July 9th, 2019 01:36 AM
Solve for integers idontknow Elementary Math 4 June 2nd, 2019 06:23 PM
Solve in integers x,y. ultramegasuperhyper Number Theory 4 May 24th, 2011 09:19 PM
Solve in possitive integers Sara so Number Theory 3 November 12th, 2010 12:18 PM
Integers: cafegurl Elementary Math 3 January 7th, 2009 07:21 AM





Copyright © 2019 My Math Forum. All rights reserved.