Question 80
Let $n \gt 1$ 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 $x$.)
Editorial metadata note: Metadata discrepancy: the dataset year is 2014, while booklet_year is 2015. The title follows dataset classification, not a verified Belarus 2014 event date.
$$
a_k = \left\lfloor \frac{n^k}{k} \right\rfloor,
$$
are odd. (For a real number $x$, $\lfloor x \rfloor$ denotes the largest integer not exceeding $x$.)
Editorial metadata note: Metadata discrepancy: the dataset year is 2014, while booklet_year is 2015. The title follows dataset classification, not a verified Belarus 2014 event date.