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### Is there any superstable configuration in the game of life?

This question spins off of Gil Kalai's recent question on Conway's game of life for a random initial configuration.
There are numerous configurations in the game of life that are known to be ...

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### Distribution of digits of $pq$-adic idempotents (aka “automorphic numbers”)

Let $p$ and $q$ be distinct primes. By the ring of $pq$-adic integers I mean the ring $\mathbb{Z}_{pq} := \varprojlim \mathbb{Z}/(pq)^n\mathbb{Z}$ which is obviously isomorphic to $\mathbb{Z}_p ...