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If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?"

14 votes

Must Mersenne numbers be divisible by arbitrary large primes with exponent one?

This is at least as strong as the infinitude of non-Wieferich primes. Indeed, if there are only finitely many non-Wieferich odd primes and they are equal to $p_1, \ldots, p_k$, then one can choose $n$ …
Alexander Kalmynin's user avatar