Question 26
Let $n\gt 1$ be a given integer. Prove that infinitely many terms of the sequence $\left(a_{k}\right)_{k \geqslant 1}$, 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 $x$.)
$$
a_{k}=\left\lfloor\frac{n^{k}}{k}\right\rfloor
$$
are odd. (For a real number $x,\lfloor x\rfloor$ denotes the largest integer not exceeding $x$.)