March 31st, 2017, 03:15 AM  #1 
Member Joined: Aug 2015 From: Chiddingfold, Surrey Posts: 47 Thanks: 2 Math Focus: Number theory, Applied maths  An extension to FLT
A THEORETICAL EXTENSION TO FLT 1. The smallest sum of a set of four different positive integers A B C D that are related by A = INT(( Bp + Cp )1/p +0.5) and D = INT(( Ap  Bp  Cp )1/p + 0.5), A B and C being relatively prime, IS WHEN B  C = 1 2. The value of A is an expression in any positive integer p. 3. The expressions I have established by trial for p from 1 to 113 are as follows: P expression 1  8 2* p + 1 8  28 2* (p â€“ INT ((p )/3) + 1 27 â€“ 54 2* (p â€“ INT ((p + 1.5)/3)  1 53 â€“ 80 2* (p â€“ INT ((p  0.5)/3) â€“ 1 79  109 2* (p â€“ INT ((p + 0.5)/3)  1 109  ??? 2* (p â€“ INT ((p + 1.5)/3) â€“ 1 Observations: The calculated value of A is equal to B + 1 The smallest value of D is where the fractional part of A is nearest and above 0.5 except when p = 1 or 2 when D = 0 Expressions for values of p higher than 113 cannot be determined without a computer having a higher resolution than the usual 64 bit. The division by 3 will presumably apply to all values of p and is due to the fact that for four consecutive values of p above 8, there are only three different values of A one of which is duplicated. Example p A 18 25 19 27 20 29 21 29 There is an overlap between adjacent expressions since both expressions produce the same result. This is where two identical values of A are followed by another two. Elsewhere there is one other value between them. Example p A 26 37 27 37 28 39 29 39 I'd like to find a proof of my theory and would like to know if anyone can find a counter example. 
March 31st, 2017, 09:00 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,591 Thanks: 546 Math Focus: Yet to find out. 
It's hard to read. If you typeset your equations with LaTeX it would be better.


Tags 
extension, flt 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
field extension  mona123  Abstract Algebra  1  October 10th, 2015 08:49 PM 
Galoisextension?  Epsilon90  Abstract Algebra  5  December 9th, 2013 09:25 PM 
extension field  Sandra93  Abstract Algebra  5  November 19th, 2013 05:45 AM 
Q as an extension field  Sandra93  Abstract Algebra  4  November 12th, 2013 03:21 AM 
Field Extension  Bruna  Abstract Algebra  0  November 3rd, 2013 12:31 PM 