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 March 31st, 2017, 03:15 AM #1 Member   Joined: Aug 2015 From: Chiddingfold, Surrey Posts: 57 Thanks: 3 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: 1,834 Thanks: 650 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 Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post mona123 Abstract Algebra 1 October 10th, 2015 08:49 PM Epsilon90 Abstract Algebra 5 December 9th, 2013 09:25 PM Sandra93 Abstract Algebra 5 November 19th, 2013 05:45 AM Sandra93 Abstract Algebra 4 November 12th, 2013 03:21 AM Bruna Abstract Algebra 0 November 3rd, 2013 12:31 PM

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