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 March 11th, 2019, 04:46 PM #1 Newbie   Joined: Feb 2019 From: Watertown NY USA Posts: 5 Thanks: 0 Counter to the abc Conjecture Counter to the abcCounter to the abc C Conjecture (version 14). [*]The abc conjecture states:[*] [*]1.) max (|a|, |b|, |c|) =< C_e PROD_{p|abc} p^(1+e) for any e > 0. [*]2.1) C_m has an upper bound. [*]Result (complete): [*]2.2) C_m has no upper bound nor limit. [*]proof. [*]given: [*]1.) max (|a|, |b|, |c|) =< C_e PROD_{p|abc} p^(1+e) for any e > 0. [*]Let [*]3.1) a = (s_1...s_n)^v where s_i is prime [*]3.2) b = (q_1...q_h)^v where q_j is prime. [*]where v any integer > 0. [*]3.3) a + b = c [*]3.4 ) GCD(a,b) = 1 [*]Let [*]4.1) a > 2[*]4.2) b > a [*](end givens)[*] [*]5.) If p_w | abc then p_w | ab(a+b) since a + b = c. [*]6. from 5.) p_w | [s_1...s_n][q_1...q_h][t_1...t_m ] where [*]where c = t_1^(r_1)...t_m^(r_m) = (s_1...s_n)^v + (q_1...q_h)^v >= t_1...t_m. [*]7. ) c / [t_1^(r_1-1)...t_m^(r_m-1)] = t_1...t_m. [*]8.) c =< max (|a|, |b|, |c|) =< C_e PROD_{p|abc} p^(1 +e). [*]9.) PROD_{p|abc} p^(1 +e) = [(s_1...s_n)(q_1...q_h)(t_1...t_m)]^(1+e) [*]10. from (8. and 9.) ) [c] / [(ab)^(1/v)]^(1+e) =< C_e. [*]11. from 10.) t_1^(r_1)...t_m^(r_m) / [(s_1...s_n)(q_1...q_h)(t_1...t_m)] ^(1+e) =< C_e [*]or [*]12. from 11.) t_1^(r_1)...t_m^(r_m) / [(ab)^(1/v)(t_1...t_m)] < C_e. [*]13. from 12.) c / [(ab)^(1/v)(t_1...t_m)] < C_e. [*]As v increases without bound then [*](ab)^(1/v) tends to 1 and c increases without bound nor limit. [*]14 from 13.) c /[(t_1...t_m)] < C_e. [*]Recall please c = t_1^(r_1)...t_m^(r_m). [*]If c increases without bound then c /[(t_1...t_m)] also increases w/out bound and therefore C_e hasn't a boundry or BOUND. [*]the proof complete. [*]Simon C. Robe[/LEFT][/LEFT][/LIST][/SIZE][/LIST][/LEFT] Tags abc, conjecture, counter 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 Jaket1 Abstract Algebra 1 March 2nd, 2018 10:18 AM guranbanan Algebra 4 September 19th, 2015 06:36 AM AceCop Probability and Statistics 2 January 15th, 2015 02:19 PM Modus.Ponens Real Analysis 0 May 16th, 2012 02:57 PM aloria Real Analysis 2 January 25th, 2012 05:20 AM

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