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Results tagged with nt.number-theory
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user 104044
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
12
votes
2
answers
944
views
Conjecture about harmonic numbers
I was inspired by this topic on Math.SE.
Suppose that $H_n = \sum\limits_{k=1}^n \frac{1}{k}$ - $n$th harmonic number. Then
Conjecture
Let $M$ be a set of all $n$ such that
$$H_n - \lfloor{H_n …
- 251
0
votes
0
answers
202
views
Representation of a number as a sum of co-prime numbers
Conventions
We will call the following product the canonical expansion of $a$:
$$a = \prod\limits_{p_i\in\mathbb{P}}p_i^{\alpha_i}.$$
If $a$ and $b$ are co-prime we write
$$a \perp b.$$
$\beth$ …
- 251