The probability that $s$ integers are relatively $r$-prime for a class of probability distributions on the integers

For each real number $t>1$, one can define a probability distribution $P_{t} = \left\{\mathrm{pr}_{t}\left(n\right)\right\}_{n\in\mathbb{N}}$ by $\mathrm{pr}_{t}\left(n\right) = \displaystyle{\frac{n^{-t}}{\zeta\left(t\right)}}$. This class of probability functions was studied by Golomb in [1]. In this post, we will prove a theorem about relatively $r$-prime … Continue reading →