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Omni-MATH / Does there exist an irrational number α>1 such that leftlflooralpha^{n}rightrfloor equiv 0 quad(bmod 2017) for all integers n≥1 ?

Problem

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problem

Does there exist an irrational number α>1\alpha>1 such that \(\left\lfloor\alpha^{n}\right\rfloor \equiv 0 \quad(\bmod 2017)\) for all integers n≥1n \geq 1 ?
Plain-text mathematical notation (without MathML)
Does there exist an irrational number α>1 such that \(\left\lfloor\alpha^{n}\right\rfloor \equiv 0 \quad(\bmod 2017)\) for all integers n≥1 ?
Original LaTeX notation
Does there exist an irrational number $\alpha>1$ such that \(\left\lfloor\alpha^{n}\right\rfloor \equiv 0 \quad(\bmod 2017)\) for all integers $n \geq 1$ ?

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Source and history

task_id
672903bf-9439-5a99-8183-3f7e2b4a15f8
task_key
test--672903bf-9439-5a99-8183-3f7e2b4a15f8
task_revision_id
1
config / split
/ test

Official source

initial import