
Number Theory Number Theory Math Forum 
 LinkBack  Thread Tools  Display Modes 
April 17th, 2015, 09:08 AM  #1 
Newbie Joined: Apr 2015 From: United States Posts: 8 Thanks: 0  Odd numbers that can be represented in only one/two ways as difference of squares
a) Find (with proof) all odd numbers that can be represented in only one way as a difference of two squares. I know that the answer to this part lies in the primes, because there is only one way to multiply to get a prime number. Just not sure how to prove it. b) Find (with proof) all odd numbers that can be represented in only two ways as a difference of two squares. I believe that the proof to this part would have something to do with four factors, (let's say a,b,c,d) where n is an odd number and a(d)=n, and b(c)=n. But I'm not too sure where to go after that? Thank you in advance! 
April 17th, 2015, 11:00 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,780 Thanks: 1025 Math Focus: Elementary mathematics and beyond 
a) primes and perfect squares that are semiprimes. b) semiprimes that are not perfect squares. This excludes using 0 as a perfect square. Consider solving x  a = one factor, x + a = another factor. Last edited by greg1313; April 17th, 2015 at 12:22 PM. 
April 18th, 2015, 09:17 AM  #3  
Senior Member Joined: Mar 2012 Posts: 572 Thanks: 26  Quote:
Prime Numbers: Is the difference of two squares always composite?  
April 27th, 2015, 12:30 AM  #4 
Senior Member Joined: Nov 2013 From: Germany Posts: 179 Thanks: 1 Math Focus: Number Theory  all odd numbers are difference of two perfect squares
a*b = ((a+b)/2)²((ab)/2)² a*b = odd number q.e.d. 
April 27th, 2015, 04:27 PM  #5 
Senior Member Joined: May 2013 From: España Posts: 151 Thanks: 4 
Hello. If you may be interested. Machine of test of prime numbers There is a demonstration, compatible with your question. Regards. 

Tags 
difference, numbers, odd, one or two, represented, squares, ways 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Difference of squares?  Vaki  Algebra  1  May 2nd, 2014 05:51 AM 
Can all numbers be represented by (a^n) +/ (b^m)?  karpmage  Number Theory  6  November 20th, 2012 11:22 AM 
Difference of squares help and 4 term difficult question.  link107  Algebra  3  February 11th, 2012 09:36 PM 
What is the history of the difference of 2 squares?  e36guy  Calculus  2  October 24th, 2010 07:01 AM 
Difference of Squares  abhijith  Number Theory  2  January 13th, 2010 06:43 AM 