Am Dienstag, 21. Februar 2017 13:23:04 UTC+1 schrieb burs...@gmail.com: > We only have D_n =\= (105)^(1/3) for each n, since > (105)^(1/3) is an irrational number, whereas D_n > for each n is a rational number.
Well we could also have D_n =\= r, for a rational r, when r doesn't have an exact finite representation. For example 0.333... = 1/3, here D_n =\= r, although r rational.
But when r is irrational, we know for sure D_n =\= r, irrespective of the integer basis. If we consider non- integer basis, what Erdös et al. did, things are different.