MathDB

Let

n > 1

be a given integer. Prove that infinitely many terms of the sequence

(a_k )_{k\ge 1}

, defined by

a_k=\left\lfloor\frac{n^k}{k}\right\rfloor,

are odd. (For a real number

x

\lfloor x\rfloor

denotes the largest integer not exceeding

x

.)
Proposed by Hong Kong

N4