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lvl10720-Turquoise
20-Turquoise
September 26, 2022
Solved

Solve Iterative Equation on Natural Numbers ?

  • September 26, 2022
  • 2 replies
  • 2864 views

Hi, Everyone.
From the following:

Iterative Equation on Natural Numbers.PNG

How to Solve the Iterative Equation on Natural Numbers ?
Thanks in advance for your time and help.
Best Regards.
Loi.

Best answer by Werner_E

While cleaning up I noticed that I forgot to post the solution using Euklids algorithm. So before the file is deleted, I post it here.

Here we have no problem with numbers too high, as it seems.

 

2 replies

W
Werner_E25-Diamond I
25-Diamond I
September 26, 2022

Your definition seems not define series of numbers.

Its NOT defined what the NEXT pair (a1; b1) would be.

Is it (165; 238) or should it be (877; 1265) or would you rather like it to be (1589; 2292) ?

The general solution is a.1=165+k*712 and b.1=238+k*1027 with k being any integer.

 

If you settle for the smallest positive numbers, a first hack could be

Werner_E_1-1664211429627.png

 

 

Not much error checking or whatsoever and the 'math' method used is not Euklid or congruences but simple pure brute force 😉

 

 

L
lvl10720-TurquoiseAuthor
20-Turquoise
September 27, 2022
@Werner_E wrote:

Not much error checking or whatsoever and the 'math' method used is not Euklid or congruences but simple pure brute force 😉

  With big numbers then:

Iterative Equation (2).PNG

(Attach ***.xmcd please)

Best Regards.

Loi.

 

 

 

W
Werner_E25-Diamond I
25-Diamond I
September 27, 2022

Interesting error message. No idea what it should mean and why it pops up.

Solution: Don't use too high numbers 🙂

W
Werner_E25-Diamond IAnswer
25-Diamond I
October 5, 2022

While cleaning up I noticed that I forgot to post the solution using Euklids algorithm. So before the file is deleted, I post it here.

Here we have no problem with numbers too high, as it seems.

 

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