MATH: Thue's Lemma, Corollaries and Few Consequences
Updated: Jul 8, 2020
By Bruno;
Recently, I have discussed with David about oddly named theorems; for example: Karamata's theorem, Cauchy-Schwartz inequality, Zsigmondy's theorem, Shuur's inequality etc. But for some reason(that I don't really understand), he couldn't stop laughing at Thue's Lemma, and it gave me the idea of posting something about it.
Let me introduce this lemma to the reader:
Now the question is: "what are this theorem's applications?", here I go with an example:
Whaaaaaaaat? Is this really proved by Thue's Lemma? The answer is yes! Here we go:
See that? It seems great! For me it is awesome how a inequality/congruence theorem can prove such a strong claim. But I think this is everything for today; Because I am in a little hurry now... By the way, I would like your feedback about this new style I am taking for writing the text, as I am not used to HTML. I will also let here below a short .pdf about thue's lemma (if it interested the reader):
Obs: it can also be found by searching: http://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvMy8yL2QzYjEzOGM0ODE3YzYwZGU4NGFmOTEwZDc0ZGNhODRjOGMyMzZlLnBkZg==&rn=dGh1ZS12NC5wZGY=
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