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Tagged with conjectures diophantine-equations
10 questions
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Conjecture about some recurrent primes
I want to know if there are conjectures similar to this one, I know there is the Bell primes conjecture or Gardner conjecture (mentioned in this page https://en.wikipedia.org/wiki/Bell_number), but ...
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How would one go about solving this conjecture concerning exponential Diophantine equations?
I’ve been working on the Collatz Conjecture, and I believe I’ve reduced it to a more tractable problem. Unless there are some errors I’ve overlooked, I have managed to reduce the Collatz Conjecture to ...
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Does the equation $\sigma(\sigma(x^2))=2x\sigma(x)$ have any odd solutions?
This question was posted in MSE in early August 2020. It did garner several upvotes, but did not receive any responses. I have therefore cross-posted it here, hoping that it gets answered.
Let $\...
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Is new $n$-conjecture as follows correct?
Given a positive integer $P>1$, let its prime factorization be written as$$P=p_1^{a_1}p_2^{a_2}p_3^{a_3}\cdots p_k^{a_k}.$$
Define the functions $h(P)$ by $h(1)=1$ and $h(P)=\min(a_1, a_2,\ldots,...
- 1,776
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Is the conjecture $min(A,B) \le rad(ABC)$ new and correct? [closed]
$\DeclareMathOperator\rad{rad}$Conjecture: If $A, B, C$ are positive integers with $\gcd(A, B)=1$, $\gcd(B, C)=1$, and $\gcd(C, A)=1$, and if $A+B=C$, then $\min(A,B) \le \rad(ABC)$.
If the ...
- 1,776
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A generalization of Lander, Parkin, and Selfridge conjecture
My question: Are the conjectures as follows correct?
Given a positive integer $P>1$, let its prime factorization be written
$$P=p_1^{a_1}p_2^{a_2}p_3^{a_3}...p_k^{a_k}$$.
Define the ...
- 1,776
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Solve this diophantine equation: $m^4+n^4=10m^2n^2+1$
t's probably common knowledge that there are Diophantine equations which do not admit any solutions in the integers, but which admit solutions modulo nn for every nn. This fact is stated, for example,
...
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1
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Question in the setting of generalized Diophantine $m$-tuples
As an amateur I am not quite sure should I post a question on the site for professional mathematicians but if the question is not appropriate for this site you can freely migrate it to ...
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13
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2
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On Generalizations of Fermat's Conjecture
We know the following facts:
(1) For all $1\leq n\leq 2$ the equation $x_{1}^{n}+x_{2}^{n}=x_{3}^{n}$ has a solution in $\mathbb{N}$.
(2) For all $3\leq n$ the equation $x_{1}^{n}+x_{2}^{n}=x_{3}^{n}...
user36136
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A sequence based on Catalan–Mihăilescu problem
It was conjectured by Catalan in 1844 that the only solutions of the equation $x^a-y^b=1$ over variables $a,b,x,y\in\mathbb{N^+}$ are trivial ones: $3^1-2^1=1$ and $3^2-2^3=1$. The conjecture was ...
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