All Questions

Let us fix a positive integer $q$, and let us define a functions $P: \mathbb{Z}\times \mathbb{N} \to \mathbb{Z}$ as follows: $$ P(s,t) := \sum_{j=1}^t \left\lfloor \frac{j (s-1) + t}{q} \right\rfloor$$...

Let us fix a natural number $N>1$ and $a_1, \ldots, a_n$ natural numbers satisfying $0 \leq a_i < N$, with the property that $1+ \sum a_i$ is divisible by $N$. Let $\phi$ be the Euler totient ...

Let's consider the unique decomposition of a natural number $\,m\,$ into its prime factors: $$\prod_k {p_k}^{\alpha_k}$$ Then, let's define the following arithmetic function (completely additive) $\,g:...