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For questions about factorization, the decomposition of mathematical objects (e.g. natural numbers, polynomials) into products of smaller objects (e.g. primes, lower degree polynomials).

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