Jump to content

Talk:Tijdeman's theorem

Page contents not supported in other languages.
From Wikipedia, the free encyclopedia

I'm pretty sure the statement about "consecutive is essential" is false. The statement for any k should follow easily from an effective version of Baker's Theorem on linear forms in logarithms, found in, say Baker's 1975 book "Transcendental Number Theory"134.10.114.3 (talk) 03:28, 15 July 2011 (UTC)[reply]

Nope. The statement for any k is an open problem which would follow from Pillai's conjecture (see article on Catalan's conjecture, now Mihăilescu's theorem), and Pillai's conjecture would follow from the ABC conjecture. Richard Gill (talk) 13:09, 13 September 2012 (UTC)[reply]

Approach with Sum of gnomons (x^n-(x-1)^n) (I call Complicate Modulus Algebra)

[edit]

To show how intriguing I found my "Complicate Modulus Algebra" method, I propose here how to work on the

Generalized Tijdeman problem

1) With: n,m = Even >=2

As I've shown:

and:

So we can immediately make:

Or:

So, once again, K can be just a sum of 2x-1 terms...

2) The cases [B]n,m with one, or both, ODDS[/B], is more complicate to be solved since as I've shown (here in case both are Odd):

and:

So we have to solve:

That is little more tricky to be reduced.

References

[edit]

The only source for this article is to a non-online reference. Can anyone provide something clickable and checkable? wikipediatrix 19:26, 22 August 2006 (UTC)[reply]

I added a number of references including a clickable reference to a survey paper on the history of Catalan's conjecture. Richard Gill (talk) 13:07, 13 September 2012 (UTC)[reply]