For questions concerning a specific proof, asking for verification, identifying errors, suggestions for improvement, etc.

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3
votes
2answers
163 views
+50

A natural number $n>2$ is a prime iff $\prod_{k=1}^{n-1} k \equiv n-1 \pmod {\sum_{k=1}^{n-1} k}$

Is this proof acceptable ? Theorem 1 (Wilson). A natural number $n>1$ is a prime iff: $$(n-1)! \equiv -1 \pmod n.$$ Theorem 2. A natural number $n>2$ is a prime iff: ...
0
votes
1answer
30 views
+100

Conditional independence given elementary events implies conditional independence given $\sigma $-algebra

Proposition: Let $X$ be a continuous markov chain with discrete state space $S$. Let $Z$ be the corresponding jump chain and $\left\{ {{W_i},i \in \mathbb{N}} \right\}$ its holding times. Let ...