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#51 2024-04-18 21:07:07

AnthonyRBrown
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Registered: 2024-03-09
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Re: Fermats Last Theorem Demonstration! by, Anthony.R.Brown (1998 Solved )

It's all a Mystery ? Like trying to get blood out of a stone!

The Ruddest in the classroom...just might be the Genius! smile

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#52 2024-04-23 01:16:06

phrontister
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From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,823

Re: Fermats Last Theorem Demonstration! by, Anthony.R.Brown (1998 Solved )

AnthonyRBrown wrote:

It's all a Mystery ? Like trying to get blood out of a stone!

Indeed! big_smile

phrontister wrote:

Absolute accuracy is required for all digits (right up to and including the units digit)

The rounding that occurs once QB64's double-precision limit is reached has enabled me to manufacture the following two X³ + Y³ = Z³ 'solutions' (I adapted your FLT code):

Ha5Ip5Pl.png

08LAvzVl.png

Just BASIC (a scaled-down freeware version of Liberty BASIC) can handle HUGE numbers accurately, making 'solution' manufacturing rather difficult!

Here are images of JB's output for the same X, Y & Z input as for the above QB64 images:

ru7us2Rl.png

NvFEkcfl.png

So, no JB solutions there.

Btw, the yellow highlighted portions denote groups of similar digits.

Last edited by phrontister (2024-04-23 01:25:12)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#53 2024-04-23 05:13:50

AnthonyRBrown
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Registered: 2024-03-09
Posts: 50

Re: Fermats Last Theorem Demonstration! by, Anthony.R.Brown (1998 Solved )

It never gives up! sad

The Ruddest in the classroom...just might be the Genius! smile

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#54 2024-04-23 11:43:34

phrontister
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From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,823

Re: Fermats Last Theorem Demonstration! by, Anthony.R.Brown (1998 Solved )

AnthonyRBrown wrote:

It never gives up! sad

But wait...there's more! big_smile

AnthonyRBrown wrote:

The most important numbers are the end numbers in brackets () the reason they are the most important is because they are the end of the process for making cube numbers! they are if you like the TRUTH numbers! its a bit like the numbers go round and round mathematically,and eventually make a whole cube number!

Ok. So, given QB64's (mis)handling of numbers that are too large for it, I thought I'd post an example demonstrating the inaccuracies that can occur in QB64 coding with the all-important last-digit TRUTH numbers in cases where the 16-digit double-precision accuracy boundary is breached: 

GOfduw1l.png

The Program A segment of that image shows QB64's accurate output of the last digit of X & Y values, compared with the inaccurate output of the last digit of Z values, each of which overstep the double-precision boundary.

In Program B of that image, all X,Y,Z values overstep the double-precision boundary, hence all those inaccuracies.

There are no such inaccuracies in the Just BASIC image below, because those same X,Y,Z values that I used in QB64 (see the image above) are within JB's HUGE upper precision limit...whatever that is! dizzy

IwAtdTVl.png

Last edited by phrontister (2024-04-23 13:33:16)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#55 2024-04-23 15:47:14

AnthonyRBrown
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Registered: 2024-03-09
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Re: Fermats Last Theorem Demonstration! by, Anthony.R.Brown (1998 Solved )

2024-04-10 11:18:46
AnthonyRBrown

Posts: 46
The FLT Demonstration program I made was made FREE! on a budget! It satisfies to show the Three Patterns A,B,C for the accuracy of the program up to certain level.

Most people read all the threads,and then walk away! sad

The Ruddest in the classroom...just might be the Genius! smile

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#56 2024-04-23 21:12:27

phrontister
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From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,823

Re: Fermats Last Theorem Demonstration! by, Anthony.R.Brown (1998 Solved )

AnthonyRBrown wrote:

Most people read all the threads,and then walk away! sad

But I'm still here! big_smile

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#57 2024-04-23 22:45:50

AnthonyRBrown
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Registered: 2024-03-09
Posts: 50

Re: Fermats Last Theorem Demonstration! by, Anthony.R.Brown (1998 Solved )

Truth will out.

The Ruddest in the classroom...just might be the Genius! smile

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#58 2024-04-24 09:40:21

phrontister
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From: The Land of Tomorrow
Registered: 2009-07-12
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Re: Fermats Last Theorem Demonstration! by, Anthony.R.Brown (1998 Solved )

AnthonyRBrown wrote:

Truth will out.

Nae doot, mon! up

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#59 Yesterday 00:27:53

phrontister
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From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,823

Re: Fermats Last Theorem Demonstration! by, Anthony.R.Brown (1998 Solved )

phrontister wrote:

The rounding that occurs once QB64's double-precision limit is reached has enabled me to manufacture the following two X³ + Y³ = Z³ 'solutions' (I adapted your FLT code):

I've explored that further, and found that manufacturing X³ + Y³ = Z³ 'solutions' for your QB64 program is quite easily done...like so:
Start with the following base numbers:
   (a) X¹ = a 17-digit number.
   (b) Y¹ = X¹
        Note: {Y¹ = X¹+1}, {Y¹ = X¹+2} and {Y¹ = X¹+3} all have successively fewer 'solutions' than {Y¹ = X¹}.
   (c) Z¹ = the cube root of Z³ (just select the first 17 digits of the cube root, and round up the last digit if it's >=5).

Using your latest code (post #33), I added an option to enter custom X¹,Y¹,Z¹ numbers instead of using the program's random numbers. Here's my adapted code:

I ran that code a few minutes ago, and here are a couple of images from it:

2ZuuBEtl.png
nxyIis0l.png

You'll notice when you look at my adapted code that I restricted the length of your random numbers so that their cubes display accurately, with no rounding or truncation: ie, within QB64 double-precision limits.

Last edited by phrontister (Yesterday 00:29:11)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#60 Yesterday 00:40:52

Bob
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Registered: 2010-06-20
Posts: 10,184

Re: Fermats Last Theorem Demonstration! by, Anthony.R.Brown (1998 Solved )

up

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#61 Today 08:43:56

AnthonyRBrown
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Registered: 2024-03-09
Posts: 50

Re: Fermats Last Theorem Demonstration! by, Anthony.R.Brown (1998 Solved )

Proving Fermat' s Last Theorem (almost) in just 2 minutes !

https://www.youtube.com/watch?v=EymVXkPWxyc

The Ruddest in the classroom...just might be the Genius! smile

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