My Math Forum  

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

Number Theory Number Theory Math Forum

LinkBack Thread Tools Display Modes
October 10th, 2012, 05:15 AM   #1
Math Team
mathbalarka's Avatar
Joined: Mar 2012
From: India, West Bengal

Posts: 3,871
Thanks: 86

Math Focus: Number Theory
Diophantine Fun

This one's pretty challenging but not as hard as we think :

Prove that has no solution in positive integers

Hint : Consider the equation modulo 4



mathbalarka is offline  
October 10th, 2012, 06:46 AM   #2
Global Moderator
CRGreathouse's Avatar
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: Diophantine Fun

Pretty easy once you divide out common factors.
CRGreathouse is offline  
October 10th, 2012, 07:06 AM   #3
Global Moderator
Joined: Dec 2006

Posts: 19,963
Thanks: 1849

If 3 divides a + b, both a and b must be divisible by 3, so 9 divides a + b, which implies c is divisible by 3.

Hence one could divide all three variables by 3 to get another solution in integers. After sufficient repetition, one must get a = b = c = 0, so this is true to start with, showing that there is no solution in positive integers.
skipjack is offline  
October 11th, 2012, 09:24 AM   #4
Math Team
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 13,600
Thanks: 954

Re: Diophantine Fun

Originally Posted by mathbalarka

Prove that has no solution in positive integers
Geesh, if Big Pete Pythagoras looked at this quickly, he'd get a heart attack
Denis is offline  

  My Math Forum > College Math Forum > Number Theory

diophantine, fun

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Another diophantine equation harrypham Number Theory 0 May 31st, 2012 06:49 PM
diophantine x + 8x - 6x + 8 = y Pell's fish Number Theory 9 March 23rd, 2012 12:07 AM
Fun Diophantine Equations icemanfan Number Theory 1 March 14th, 2012 03:52 PM
diophantine equation islam Number Theory 4 January 11th, 2012 04:28 AM
Diophantine Fun mathbalarka Algebra 1 December 31st, 1969 04:00 PM

Copyright © 2018 My Math Forum. All rights reserved.