New answers tagged abc-conjecture
3
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Small solutions of $x^2-a^3 y^2=\pm 1$
It is better to ask one question per post. Here is the answer to Q1.
Assume that $(x,y)$ is a positive integer solution of $(1)$. Then $(x,ay)$ is a solution of $X^2-aY^2=1$. Let us restrict to $a=u^2-...
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4
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Consequences of Kirti Joshi's new preprint about p-adic Teichmüller theory on the validity of IUT and on the ABC conjecture
Since my preprint [Constr. IV] appeared on the arixv, I have received many questions about my work. I continue to answer these emails and I have collected many of the questions and answers in this Q&...
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49
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Global character of ABC/Szpiro inequalities
This is from my recent email to Peter Scholze in response to his post above:
My response to Peter Scholze:
I read your comments on MathOverFlow. Thank you for your kind words.
Somehow, once again, we ...
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39
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Global character of ABC/Szpiro inequalities
Mochizuki's claim is right in spirit but not stated completely rigorously. I want to explain (1) what part is not completely rigorous and (2) why this is not problematic for the analysis of any ...
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113
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Accepted
Global character of ABC/Szpiro inequalities
For concreteness, consider the $abc$-inequality with $\epsilon=1$, i.e. that there is some integer $K$ such that for all coprime integers $a,b,c$ with $a+b=c$, one has
$$abc\leq K \prod_{p|abc} p^6.$$
...
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19
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Global character of ABC/Szpiro inequalities
This is not an answer to the question but too long for a comment. It is interesting to ask if one can prove the ABC inequality just for the tuple $(1,p^n,1+p^n)$ directly for fixed $p$. ABC says
$$\...
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34
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Consequences of Kirti Joshi's new preprint about p-adic Teichmüller theory on the validity of IUT and on the ABC conjecture
My response to Mochizuki's Comments on my papers [Preprints: Construction of Arith. Holo. Strs I, II, II(1/2), III, IV. I will restrict myself to mathematics.
My work shows that Mochizuki's [IUT 1-3] ...
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