# Questions tagged [abc-conjecture]

For questions about and related to the abc conjecture.

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### Serge Lang Algebra - Generalized Szpiro Conjecture-like inequality derived from ABC Conjecture

There is a specific part of the section of Serge Lang's Algebra from Chapter IV Section 7 regarding an inequality preceding the generalized Szpiro Conjecture that confused me. How exactly are the ...
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### Why does Mochizuki insist on “forgetting the previous history of an object”?

What is the simplest (at the lowest level feasible) explanation of the approach of “forgetting the history” of a mathematical object, as used in Inter-universal Teichmüller Theory (IUTT)? Please ...
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### ABC conjecture Proof

So I have a question. Why is Shinichi Mochizuki's proof on the conjecture still not accepted? It has been 6 years, surely there must be some approval or disapproval regarding his proof? Can anyone ...
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### Square-free values of polynomials of degree 3

While reading an article by Dan Carmon on Square-free values of large polynomials over the rational function field, I tried to prove that square-free polynomials of degree $1$ and $2$ have a positive ...
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### How can the abc conjecture put constraints on the prime factors of $c$?

Let $c = a + b$ be an abc-triple $(a, b, c) \in \mathbb{N}$ with $\text{gcd}(a,b,c) = 1$, with the prime factorizations of $a$ and $b$ known. How can the abc conjecture put constraints on the prime ...
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### What mathematical conjectures broke down in an unintuitive way? [duplicate]

Conjectures are often based on inference from a few cases. A famous example is the Riemann Hypothesis which states that all zeros of the zeta function have real part 1/2. All the zeros that we've ...
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### When we try to solve the hard problem like 'ABC conjecture',should we first examine if it is a proposition that neither prove nor disprove [closed]

In mathematic logic,Godel's incompleteness theorem tell us that a proposition that neither prove nor disprove is exist.so did every famous hard problem need to be examine first?
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### A variant of the radical for integers and the abc-conjecture

Define $\mathcal P(n)=\{\{q_1\},\dots,\{q_m\}\}$ where $n=\prod_{i=1}^mq_i$ and all $q_i\in\mathbb P$. Then one can define $\displaystyle \operatorname{rad}(n)=\prod_{p\in\bigcup\mathcal P(n)}p$ and ...
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### Conjecture related to abc-conjecture, with $a<b=p^n,\,n>1$

Let $\operatorname{rad}(b)$ be the product of all distinct prime factors of $b$. The numbers $\,a,b,c\,$ is a $abc$-triple if they are coprime and $a+b=c$. One version of the abc-conjecture is then: ...
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### Video of Shinichi Mochizuki skype conference

In late 2015, Shinichi Mochizuki gave a skype conference to mathematicians about his IU Teichmuller theory. I have tried to find videos of that conference but my efforts have been in vain. Do you ...
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### Conjecture: injection from exceptional abc-triplets to natural numbers

My question A conjecture with connection to the $abc$-conjecture is about a conjectured injection from exceptional $abc$-triplets $(a,b,c)\mapsto a^2+b^2$, but this question is about a ...
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### A conjecture with connection to the $abc$-conjecture

The numbers $\,a,b,c\,$ is a $abc$-triplet if they are coprime and $a+b=c$. One version of the abc-conjecture is then: For all $\varepsilon>0$ the set $E_\varepsilon$ of all $abc$-triplets with ...
An article online says: The abc conjecture refers to numerical expressions of the type $a + b = c$. The statement, which comes in several slightly different versions, concerns the prime numbers ...