3

Part of 1996 Japan MO Finals

Problems(1)

Sequence from non-integer x is not periodic

Source: Japanese MO Finals 1996

x>1

be a real number which is not an integer. For each

n\in\mathbb{N}

a_n=\lfloor x^{n+1}\rfloor - x\lfloor x^n\rfloor

. Prove that the sequence

(a_n)

is not periodic.

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