
Math General Math Forum  For general math related discussion and news 
 LinkBack  Thread Tools  Display Modes 
January 11th, 2019, 10:18 PM  #1 
Newbie Joined: Jan 2019 From: France Posts: 2 Thanks: 0  A stronger fomulation of Fermat's Last Theorem
We consider only positive integers. The formulation is as follows: Every squared integer can be expressed as the difference of two squared integers; for powers greater than two, there is not a single integer for which an analogous statement is true. In short, every integer is a member of a Pythagorean triple. Note that for prime numbers and even semiprimes (2*odd prime), the expression is unique and consists in the former case of consecutive integers, in the latter of integers which differ by two. In other cases, there are as many expressions as there are factorisations of the squared integer into two unequal integer factors of the same parity (where 1 is considered a legitimate factor). 
January 12th, 2019, 02:07 AM  #2 
Newbie Joined: Jan 2019 From: France Posts: 2 Thanks: 0 
Examples: Prime: 17×17 = 145×145  144×144 Even semiprime: 22×22 = 122×122  120×120 Other: 12×12 = 37×37  35×35 = 20×20 16×16 = 15×15  9×9 = 13×13  5×5 

Tags 
factorisation, fermat, fomulation, integer, stronger, theorem 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Fermat last theorem  Rachanesamir  Number Theory  2  May 13th, 2015 07:46 AM 
About Fermat's Little Theorem  McPogor  Number Theory  5  December 7th, 2013 07:28 PM 
Fermat's Last Theorem  McPogor  Number Theory  15  May 31st, 2011 07:31 AM 
fermat's last theorem????  smslca  Number Theory  4  September 14th, 2010 08:00 PM 
Fermat's last theorem.  SnakeO  Number Theory  10  September 25th, 2007 04:23 PM 