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Results tagged with nt.number-theory
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user 41947
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
11
votes
1
answer
491
views
$p$-adic sums of $p$ terms
My question is inspired by this riddle: Let $p \geq 5$ be prime, and let
$$ 1 + \frac 1 2 + \frac 1 3 + \dots + \frac 1 {p-1} = \frac a b $$
where $a/b$ is the fraction expressed in lowest terms. Sh …
- 1,105
4
votes
Accepted
Determining if a number is k-rough without factoring
First of all, I don't think you should dismiss searching for a prime factor as a method for determining whether a number is $k$-rough. The Elliptic Curve Method (ECM) is a prime factorization algorith …
- 1,105
13
votes
Accepted
Small $|2^x 3^y - 5^z 7^t|$ and generalization
Baker's theorem implies that
$$ |\log (A/B)| = |\sum e_i \log p_i - \sum f_j \log q_j| > \max (e_i, f_j)^{-C} $$
where $C$ depends only on $\{p_i\}, \{q_j\}$. Since $A \leq \left( \prod p_i \right) …
- 1,105
2
votes
Density of the Klarner-Rado Sequence
I have performed a heuristic calculation of the density of the Klarner-Rado sequence. My calculation suggests that the Klarner's conjecture is false. Instead, I expect the number of terms in the Klarn …
- 1,105