All Questions
7
questions
2
votes
0
answers
173
views
Question about the collection of the prime factors of a fibonacci number
A positive integer $n$ is called pandigital , if every digit from $0$ to $9$ occurs in the decimal expansion of $n$.
Conjecture : The largest non-pandigital fibonacci-number (a fibonacci-number with ...
- 85.1k
4
votes
1
answer
120
views
If $p$ can divide $a^n+b^n+c^n$ , can $p^k$ divide it as well?
Related to this
Is there a method to decide whether a given function of the form $f(n)=a^n+b^n+c^n$ ($a,b,c$ fixed positive integers , $n$ running over the positive integers) satisfies the following ...
- 85.1k
3
votes
0
answers
131
views
Beal's conjecture $A^x+B^y=C^z$
Beal's conjecture is a generalization of Fermat's Last Theorem. It states: If $A^x + B^y = C^z$, where $A, B, C, x, y$ and $z$ are positive integers and $x, y$ and $z$ are all greater than $2$, then $...
- 75
4
votes
0
answers
114
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Conjecture on the sum of prime factors
$\text{Notations}$
Let $\pi(n)$ be the prime counting function.
Let denote $\alpha(n)$ the sum of the prime factors of $n$. (i.e. In other words, if $$n=p_1^{x_1}p_2^{x_2}...p_m^{x_m}$$ then $\alpha(n)...
user799688
2
votes
1
answer
167
views
Conjecture on $\pi(n)$ and other arithmetic functions
$\text{Notations}$
Let $\pi(n)$ be the prime countiong function.
Let $\alpha(n)$ denote the number of prime factors of $n$ and $\beta(n)$ the sum of the prime factors of $n$. In other words, if $$n=...
user799688
2
votes
1
answer
184
views
The equation $\varphi(n)=n-\log_2(1+\operatorname{gpf}(n))-\operatorname{gpf}(n)+1$ and Mersenne primes
Let $n\geq 1$ an integer, we denote the Euler's totient function as $\varphi(n)$ and the greatest prime dividing $n$ as $\operatorname{gpf}(n)$ (that it the arithmetic function defined in the ...
user243301
0
votes
1
answer
191
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For all $n$, $9^n + 25^n - 1$ has a prime factor with $7$ in its decimal representation?
Let $x_n$ be a sequence of positive integers defined by $x_n=9^n + 25^n -1$ for all $n \ge 2$
I conjectured that there exists at least one prime divisor of $x_n$ which contains $7 $ in its decimal ...
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