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 $⌊ h \times 2021^{n} ⌋$ is not divisible by $⌊ h \times 2021^{n - 1} ⌋$ ?

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