Generate many examples of Ramanujam's Diophantine Equation 1.0 
Date Added: August 09, 2013  Visits: 272 


This programme is about finding many examples of Ramanujam's Diophantine Equation. For mathematical formulas used in making this programme, I have referred to the article MATHEMATICAL MINIATURE 9.pdf by John Butcher, butcher@math.auckland.ac.nz.To circumvent the problem of editing the Greek symbols, I have replaced them with suitable alphabets.The basic equation we are trying to solve is to get the numbers :x & y and u & v and N that satisfy the Diophantine equation :x^3 + y^3 = u^3 + v^3 = Nwhere the four integers x, y, u, v have no common factor.For eg, the "lowest" Diophantine Number N of Ramanujam is :1729 = 9^3 + 10^3 = 1^3 + 12^3Another example is :(107766)^3 + (634932)^3 = (2013055)^3 + 1991671^3= 257217167508536664 (Calculator) { 2.572171675085367e+017 (Matlab) }ie, 2013055^3 = 107766^3 + 634932^3 + 1991671^3I wish to thank Prof John Butcher for his article which triggered and enabled me to write this MATLAB code for "generating" Ramanujam's Diophantine Equation Numbers. I hope that this programme will be useful to many the world over. Time permitting, I may be improving on this programme to make it suitable for generating a series of Diophantine Numbers automatically. But the base groundwork is already laid now, and we need only to build further.Q1a : I am curious to know why Prof John Butcher has said that gcd (a, b) and gcd (c, d) should be 1.In the case of his own example : 9^3 + 15^3 = 2^3 + 16^3 = 4104,intermediate calculations give a = 12, b = 3, c = 9, d = 7.See Usage Eg Case 4 below. Obviously, gcd (a, b) = 3 (not 1).But, gcd (x, y, u, v) = 1 (var name used in my programme is G_Gxy_Guv.)Also, in his second example : 33^3 + 15^3 = 2^3 + 34^3 = 39312,calculations give a = 3, b = 9, c = 9, d = 8. See Usage Eg Case 5 below.Obviously, gcd (a, b) = 3 (not 1). But, gcd (x, y, u, v) = 1.Similarly, in his 3rd example too, gcd (a, b) = 3 (not 1) !In many of my own examples with randomly chosen values, I have mixed results:In Usage Eg 2, gcd (c, d) = 9 (not 1), but, gcd (x, y, u, v) = 1.In Usage Eg 3, gcd (a, b) = 3 (not 1), but, gcd (x, y, u, v) = 3 (not 1) !Egs 7 and 8 are similar to Eg 2 ; Egs 9, 10, and 11 are similar to Eg 3.Q1b) Therefore, I would like to know the condition or constraint, which when fulfilled, will ensure that we will certainly obtainx, y, u, v such that gcd (x, y, u, v) = 1Q2 : I would also like to know how the article's Theorem 1 is used in deriving the formulae for Diophantine Numbers.It says : ... "although beneath the surface" ... ************Now added in the suite :find_x_y__p_1_mod_6.m : This function finds x and y pairs of numbers such that x2 + 3y2 = p where mod(p, 6) = 1

License: Shareware  Size: 10 KB 
Business

Astra SNesting 2.0.0
Astra SNesting software is intended for optimizing true shape nesting. The software can be used for cutting parts from metal, fabric, leather, wood, glass, stone and other sheet materials. All the features of Astra SNesting software were... 
2.59 MB  
Modules

TPG Get Posts 1.2.4
his plugin adds the ability to put a shortcode tag in a page or post and have it display a list of posts formatted similarly to the standard blog. The posts can be selected by one or more tag values to show only items relevant to the page.By... 
245.76 KB  
Medical

EMT Intermediate Exam Prep 1.1
EMT Intermediate Exam Prep is to help you prepare the Emergency Medical TechnicianIntermediate(EMTI) examination on the go. With its exclusive intuitive UI, you can take the mock test and get the exam experience on the go, plus you can set... 
819.2 KB  
Enhanced Calculators

Electrical Calculations 2.48
Electrical Calculations software provides calculations for busbar and cable ratings, static and bulk power factor correction, motor starting currents and curves, enclosure ventiation and many metric / imperial conversions and constants. Written... 
983 KB  
File Renamers

Disk Space Usage 1.9.1
It is not a secret that it is very difficult to study disk space usage of such difficult organism as PC. However with Directory Size program you can make it for a few minutes. The program advantage is its evident character, convenient interface,... 
779.36 KB  
Miscellaneous Dialup Networking Tools

CardioLog  SharePoint Usage Reports 1.19.2.0
SharePoint Usage Reports and monitoring Solution  CardioLog: Because we really know SharePoint in depth  CardioLog is designed especially for SharePoint, we know the structure, we know the internals, and we provide the true insight about what's... 
3.24 MB  
Mathematics

jExacter 1U
A scientific calculator provides calculations within a limit of 1 to 240 significant digits. Formulas are written in natural notation and are built of operators, constants and variables, and are limited to a length of 250 characters. The number... 
488.28 KB  
Mathematics

jExacter2U 2U
A scientific calculator provides calculations within a limit of 1 to 240 significant digits. Formulas are written in natural notation and are built of operators, constants and variables, and are limited to a length of 250 characters. The number... 
430.66 KB  
Utilities

duv Visual Disk Usage 2.0
duv visual disk usage draws an interactive visualization of disk usage, with display area proportional to disk space. The map may be based on directory hierarchy, uid of owner, file extension (.c, .mp3, etc.), or number of days since last access... 
54.27 KB  
Libraries

Pod::Usage 1.35
Pod::Usage, pod2usage() can print a usage message from embedded pod documentation. SYNOPSIS use Pod::Usage my $message_text = "This text precedes the usage message."; my $exit_status = 2; ## The exit status to use my $verbose_level = 0; ##... 
97.28 KB 
Scripts

Freelancer Script 5.05
Main Features: 100% Secured. Email Support (3 Years). FREE Updates (3 Years). Post projects. Featured projects. Private projects. Sealed projects. Edit/delete projects. Select freelancers.... 
5.49 MB  
Scripts

B2B Script 4.20
Main Features: 100% Secured. Email Support (3 Years). FREE Updates (3 Years). Signup Account (Registration of account). Lead generation tools (for the sellers). Email verification to... 
5.49 MB  
Scripts

B2C Script 5.06
Main Features: 100% Secured. Email Support (3 Years). FREE Updates (3 Years). The script comes with totally editable site colors, icons and graphics Multilevel categories allows extensive browsing Admin can change Category ordering or... 
5.49 MB  
Scripts

Social Networking Script 2.86
Main Features: 100% Secured. Email Support (3 Years). FREE Updates (3 Years). Registration with name, email, password, date of birth etc. User can add multiple school, college, university with start... 
5.49 MB  
Scripts

Business Networking Script 8.04
Main Features: 100% Secured. Email Support (3 Years). FREE Updates (3 Years). Ajax based interface. Profile creation. Different types of profile. Profile for jobseekers, employers and employed... 
5.49 MB  
Development Tools

VMP Viewer 1.0
This is a very rudimentary tool to visualize the VMP files generated by BrainVoyager. Useful to share files with people who do not have BV. 
10 KB  
Development Tools

Sending reports and timestamped file by emailing 1.0
main executing reference usage:[1] usage_send_mail.mIllustrates email sending with multiple separate files or single timestamped tar file. Attachment failure is properly handled, with continuation of report emailing without the attachment.[2]... 
768 KB  
Development Tools

IrisMVC 2.0 rc1
IrisMVC is an OOP PHP framework that developers can use as a strong and secure foundation to build on various web applications following the ModelViewController (MVC) pattern. It provides the basic functionality developers need, without... 
51.2 KB  
Development Tools

7Zip for Script 4.42
7Zip is a file archiver with a high compression ratio.Features: High compression ratio in new 7z format with LZMA compression Supported formats: Packing / unpacking: 7z, ZIP, GZIP, BZIP2 and TAR Unpacking only: RAR, CAB, ISO, ARJ, LZH, CHM,... 
624.64 KB  
Development Tools

Barnardextest 1.0
This file, as the Fisher's exact test, performs the exact probability test for a table of frequency data crossclassified according to two categorical variables, each of which has two levels or subcategories (2x2). It is a nonparametric... 
10 KB 