Problem #PRU-78705

Problems Algebra and arithmetic Number theory. Divisibility Divisibility of a number. General properties Methods Examples and counterexamples. Constructive proofs Calculus Real numbers Integer and fractional parts. Archimedean property
 14–16  3.0

Problem

Does there exist a number \(h\) such that for any natural number \(n\) the number \(\lfloor h \times 2021^n\rfloor\) is not divisible by \(\lfloor h \times 2021^{n-1}\rfloor\)?