Math Is Fun Forum

You've made numerous errors in the above calculations, and I've shown the correct figures below.

All my calculations were made in Mathematica, and I've confirmed a random selection of them with a high-precision calculator (freeware) I have that is accurate to 10051 digits.

Your Pattern (B) errors: All of your DIFFERENCE entries are incorrect for 2 reasons:
1. Absolute accuracy is required for all digits (right up to and including the units digit), but you have used the 16-digit overflow notation of e+36 and e+28 that truncates accuracy to only the first 16 digits.
2. In your 'First (10) Numbers' group, only the first 10 or so digits are correct, while in your 'Second (10) Numbers' group only the first 3 digits are correct (except the last, which has just 2).

Your Pattern (C) errors: All of your entries are incorrect for 2 reasons:
1. Absolute accuracy is required for all digits (right up to and including the units digit), but you have used the 16-digit overflow notation of e+41 and e+42 that truncates accuracy to only the first 16 digits.
2. In both groups of 10 numbers, you've used the wrong DIVIDE COUNT of 1 to 10. The correct divisor in each case is the nth position of the base number in the list of numbers to be cubed. In the case of the 'First (10) Numbers' group, the base numbers are 1030561 to 1030570, and in the case of the 'Second (10) Numbers' group, the base numbers are 107276675808311 to 107276675808320.

See your post #1:

====================================================================================================

The following are my corrected entries:

  Your First (10) Numbers Pass as PATTERN (B) = 7,9,7,1,1,7,9,7,1 in brackets ()

  1234570577558077903820610782563862681159521
  DIFFERENCE = 8385742522860428117484726426646630687: PATTERN B = (7)
  1234578963300600764248728267290289327790208
  DIFFERENCE = 8385791345349132795871201046853220459: PATTERN B = (9)
  1234587349091946113381524138491336181010667
  DIFFERENCE = 8385840168074711060970510438596636437: PATTERN B = (7)
  1234595734932114188092585109001774777647104
  DIFFERENCE = 8385888991037163832179319961379931021: PATTERN B = (1)
  1234604120821105225256417288321736157578125
  DIFFERENCE = 8385937814236492028896971368747538931: PATTERN B = (1)
  1234612506758919461748446185293104905117056
  DIFFERENCE = 8385986637672696570525482813479319767: PATTERN B = (7)
  1234620892745557134445016710775918384436823
  DIFFERENCE = 8386035461345778376469548852784605609: PATTERN B = (9)
  1234629278781018480223393180324771169042432
  DIFFERENCE = 8386084285255738366136540453496253657: PATTERN B = (7)
  1234637664865303735961759316865224665296089
  DIFFERENCE = 8386133109402577458936504997264703911: PATTERN B = (1)
  1234646050998413138539218253370221930000000

  Your Second (10) Numbers Pass as PATTERN (B) = 7,9,7,1,1,7,9,7,1 in brackets ()
               
  1234570577557885867934842042214716618784231
  DIFFERENCE = 34524855517444697465677443097: PATTERN B = (7)
  1234570577557920392790359486912182296227328
  DIFFERENCE = 34524855517445341125732292969: PATTERN B = (9)
  1234570577557954917645876932253308028520297
  DIFFERENCE = 34524855517445984785787142847: PATTERN B = (7)
  1234570577557989442501394378238093815663144
  DIFFERENCE = 34524855517446628445841992731: PATTERN B = (1)
  1234570577558023967356911824866539657655875
  DIFFERENCE = 34524855517447272105896842621: PATTERN B = (1)
  1234570577558058492212429272138645554498496
  DIFFERENCE = 34524855517447915765951692517: PATTERN B = (7)
  1234570577558093017067946720054411506191013
  DIFFERENCE = 34524855517448559426006542419: PATTERN B = (9)
  1234570577558127541923464168613837512733432
  DIFFERENCE = 34524855517449203086061392327: PATTERN B = (7)
  1234570577558162066778981617816923574125759
  DIFFERENCE = 34524855517449846746116242241: PATTERN B = (1)
  1234570577558196591634499067663669690368000

 
  Your First (10) Numbers Pass as PATTERN (C) = 1,4,9,6,5,6,9,4,1,0 in brackets ()

  1234570577558077903820610782563862681159521 : DIVIDE COUNT 1030561 = 1197959730242147630097209949303207361 (1)
  1234578963300600764248728267290289327790208 : DIVIDE COUNT 1030562 = 1197966704866471657453630414560491584 (4)
  1234587349091946113381524138491336181010667 : DIVIDE COUNT 1030563 = 1197973679524634702955107197222621209 (9)
  1234595734932114188092585109001774777647104 : DIVIDE COUNT 1030564 = 1197980654216636897943829892177268736 (6)
  1234604120821105225256417288321736157578125 : DIVIDE COUNT 1030565 = 1197987628942478373762370435947015625 (5)
  1234612506758919461748446185293104905117056 : DIVIDE COUNT 1030566 = 1197994603702159261753683107431358016 (6)
  1234620892745557134445016710775918384436823 : DIVIDE COUNT 1030567 = 1198001578495679693261104528648713169 (9)
  1234629278781018480223393180324771169042432 : DIVIDE COUNT 1030568 = 1198008553323039799628353665478426624 (4)
  1234637664865303735961759316865224665296089 : DIVIDE COUNT 1030569 = 1198015528184239712199531828402780081 (1)
  1234646050998413138539218253370221930000000 : DIVIDE COUNT 1030570 = 1198022503079279562319122673249000000 (0)

  Your Second (10) Numbers Pass as PATTERN (C) = 1,4,9,6,5,6,9,4,1,0 in brackets ()

  1234570577557885867934842042214716618784231 : DIVIDE COUNT 107276675808311 = 11508285172481458545216672721 (1)
  1234570577557920392790359486912182296227328 : DIVIDE COUNT 107276675808312 = 11508285172481673098568289344 (4)
  1234570577557954917645876932253308028520297 : DIVIDE COUNT 107276675808313 = 11508285172481887651919905969 (9)
  1234570577557989442501394378238093815663144 : DIVIDE COUNT 107276675808314 = 11508285172482102205271522596 (6)
  1234570577558023967356911824866539657655875 : DIVIDE COUNT 107276675808315 = 11508285172482316758623139225 (5)
  1234570577558058492212429272138645554498496 : DIVIDE COUNT 107276675808316 = 11508285172482531311974755856 (6)
  1234570577558093017067946720054411506191013 : DIVIDE COUNT 107276675808317 = 11508285172482745865326372489 (9)
  1234570577558127541923464168613837512733432 : DIVIDE COUNT 107276675808318 = 11508285172482960418677989124 (4)
  1234570577558162066778981617816923574125759 : DIVIDE COUNT 107276675808319 = 11508285172483174972029605761 (1)
  1234570577558196591634499067663669690368000 : DIVIDE COUNT 107276675808320 = 11508285172483389525381222400 (0)

Hi AnthonyRBrown;

I'm simply pointing out a discovery I made about cube numbers and a particular sequence of non-cube numbers: that both sets of numbers satisfy the A,B,C Patterns. I had thought that your Patterns only applied to cubes.

A couple of things about your program:
   1. I don't fully understand your code, but the upper accuracy limit appears to be 16 digits, which would mean that it probably can't tell if a greater-than-16-digit-number is a cube or not: eg, can it identify the cube in the following two numbers? (one is a cube, the other is a non-cube power, the two numbers are from different groups of ten and are the first number in their group, and both groups satisfy the A,B,C Patterns):
          1234570577558077903820610782563862681159521;
          1234570577558058492212429272138645554498496.

   2. I tested the accuracy of FERMFILE's contents, and all was good until 208065^3, which returned 9007351116674624. That is obviously incorrect, as the units digit must be 5.
      (a) Thereafter, every second cube was out by +/- 1: eg,

           208067^3 = 9007610865436764 (should end in 3)
           208068^3 = 9007740741690432 ok
           208069^3 = 9007870619192508 (should end in 9)
           208070^3 = 9008000497943000 ok
           208071^3 = 9008130377941912 (should end in 1)
           208072^3 = 9008260259189248 ok
           208073^3 = 9008390141685016 (should end in 7)
           208074^3 = 9008520025429224 ok
           208075^3 = 9008649910421876 (should end in 5)

There are 3706 errors from 208065^3 to 215443^3 (9999934692543307), which is the highest cube before the start of the 16-digit overflow that is denoted by "D+16" (etc).

Btw, FERMFILE gave the same results after a computer cold restart.

Sorry about that! Yes, in my haste last night, waaay after midnight and while yawning my way through the exercise, I clumsily overlooked the impact that my changes would have on FERMFILE. And, being a slow learner, I'm here again waaay after midnight, trying to fix my so-called 'fix'!

But, I think I've actually fixed it this time, as everything I checked (which I hope was all the nessessary bits) works fine, including FERMFILE.

Here are our two programs for comparison (your original update for Patterns A,B,C, and my edited version of it):

My edited program (including the subsequent edits described below the hide box):

My subsequent edits that I referred to above:

1. I replaced your lines 123-132 with lines 124 & 125:
If RUNCUBESTEST = "T" Or RUNCUBESTEST = "t" Then GoTo CUBETESTLB
If RUNCUBESTEST = "M" Or RUNCUBESTEST = "m" Then GoTo MAKECUBESLB

2. I replaced your lines 342-345 with lines 335-340:
If RUNCUBESTEST = "M" Or RUNCUBESTEST = "m" Then
Print
Print ; " THE CUBE NUMBERS HAVE BEEN SAVED TO FERMFILE.TXT "
Print
Print " IF YOU RUN THE PROGRAM AGAIN THE PREVIOUS FERMFILE.TXT WILL BE ERASED! "
End If

3. I deleted line 11: 'Dim Shared RUNMAKECUBES As String' (after Change 2, QB64 flagged it as being an unused variable).

4. I replaced your lines 348,349 with line 343:
If QUIT = "Q" Or QUIT = "q" Then End

You'll notice that in Changes 1, 2 & 4 I included the boolean 'Or', and in Change 2 I trimmed out the superfluous 'If...Then' lines (closing it off with an 'End If'). I did that mainly because I learnt BASIC on an old pocket computer with an extreeemely tiny memory and got into the habit of minimising code.

My edits are only suggestions, of course...you may prefer your more expanded style.

Hi AnthonyRBrown;

Your updated program seems to run well!

I haven't had time to look at it all that much, but I noticed you didn't include a fix for this:

This is the part of your code I was referring to (now lines 123 to 132 in the update):

And here's the sort of fix I've got in mind, replacing the above code:

INPUT " ENTER (T) TO RUN CUBE NUMBER TEST or (M) TO RUN CUBE NUMBER MAKER.."; RUNCUBESTEST
CLS
IF RUNCUBESTEST = "T" THEN GOTO CUBETESTLB
IF RUNCUBESTEST = "t" THEN GOTO CUBETESTLB
IF RUNCUBESTEST = "M" THEN GOTO MAKECUBESLB
IF RUNCUBESTEST = "m" THEN GOTO MAKECUBESLB

That would help people to see, and run, the 'hidden' 2nd option, instead of maybe stumbling upon it.

That's the link to the webpage containing the image, not to the image on it. It shouldn't have the .jpeg extension.

Here's an image of that webpage. It's just a small version of it, done by using the letter 't' (for small) size modifier before the '.jpeg' extension:

The link to the image on that webpage is this:

[img]https://i.imgur.com/xx9dW9G.jpeg[/img]

And here's the image:

Following on from my previous post...

This is the link text from my previous post:

[img]https://i.imgur.com/7NtStGD.jpeg[/img]

Clicking the 'Preview' button shows that the image will be HUGE, so I'll place the size modifier letter "l" (for "large") before the image extension (".jpeg") to reduce the image size from huge to large (I described that Imgur feature here).

With the size modifier "l" added, my link (including img tags) becomes:

[img]https://i.imgur.com/7NtStGDl.jpeg[/img]

Now I'll copy that, and paste it into this post.

Here goes...

And there's the image.

I assume you wanted the image to display...which it can't, for 2 reasons:
   1. Your img tags have spaces, which render them invalid.
   2. The link is to the webpage containing the image and not to the image itself.

The image link (see below) is very different from your webpage link, as you can see:

[img]https://i.imgur.com/7NtStGD.jpeg[/img]

Just copy the above text and paste it into a post to display the image.

Alternatively, you could've put your webpage link in url tags, like so:

[url=https://i.imgur.com/a/gpB0TL4]Graph of Two functions[/url]

Here it is: Graph of Two functions.
   1. The link is clickable, making it easier to view the webpage.
   2. I gave the link a title (ie, your thread title), and the link shows how that's done.

An image will only display on a forum post if the actual image address (ie, the image url) is enclosed in 'image tags'...as shown in my Post #9 above. Also see instructions about that here (about halfway down the page): BBCode).

The two addresses you gave are to the webpage containing the image, not to the image itself.

The image url will have an image extension (eg, ".jpeg"), but merely adding that extension to a webpage address, as you did, doesn't work.

In fact, the image address looks entirely different from the webpage address you gave, and it's this:

[img]https://i.imgur.com/7NtStGD.jpeg[/img]

Btw, I obtained that address with my laptop, on which it's easily done with a couple of mouse clicks. I don't have a smartphone.

In other posts, amnkb and Bob have tried to help you obtain an image address via your smartphone, but the process is a bit tedious and you said here "Thanks but I am not going through all those steps".

HOWEVER, on your post #5, the link you gave is an image address, not just one to the webpage containing the image!!! How did you get that?

If you can repeat that process...

Hi A.R.B.;

I ran your BASIC program from the code you gave in post #2...

...and here's one of the results:

Xn1 = 7806
Yn1 = 845
Zn1 = 4215

I had expected Zn1 to be 8651 (ie, the sum of Xn1 and Yn1), but it isn't. That's because your 'RANDOM NUMBER ROUTINE' finds random numbers for all three variables Xn1, Yn1 & Zn1.

This means that Zn1's value isn't related to those of the other two variables, and in many cases is less than the sum of the other two cubes! Therefore, and given the infinite range of random numbers involved, I think there's less than about 1/∞ chance that your program will ever find an occasion of Xn3 + Yn3 = Zn3.

Maybe if your program started looking for an instance of an integer cube root of (Xn3 + Yn3) it would have a greater chance of success...but probably not, coz this is the realm of infinity!

Hi Kerim;

Yes, I basically did the same as you in Excel.

Also, here's a Mathematica formula, with constraints that a & b are positive integers:

In[1]:= Reduce[17a+29b==1000&&a>0&&b>0,{a,b},Integers]

Out[1]= (a==23&&b==21)||(a==52&&b==4)

Yaaawn! Yessssss......

Oops...I just saw it under the 'Quick reply' box!