Erdős problem #257: all base irrationality of the reciprocal Mersenne subseries for every infinite reciprocal summable support, with weighted mass and positive cover extensions, achievement set geometry, and exact greedy membership criteria
Source: github.com/wcook04/plectis-erdos-lean/tree/52f29ad173b04e3b…
Erdős problem 257 asks whether the sum over a in A of 1/(2^a - 1) is irrational for every infinite set A of positive integers. The principal theorem compared here settles the whole reciprocal summable regime at every integer base: if A is infinite and the sum over a in A of 1/a converges, then the sum over a in A of 1/(b^a - 1) is irrational for every integer b at least 2 (ReciprocalSupport.irrational_supportPowerSeries_of_summable_reciprocal). No pairwise coprimality, periodicity, density, or powerful support hypothesis appears. Paul Erdős printed the pairwise coprime case of exactly this…
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