Question 45
Let $n$ be a nonnegative integer and let $r$ be an odd number. Show that there is some $0 \leq i \lt 2^{n}$ such that
$$
\binom{2^{n}+i}{i} \equiv r \pmod{2^{n+1}}.
$$
$$
\binom{2^{n}+i}{i} \equiv r \pmod{2^{n+1}}.
$$
MathNet 2022-part-06 — 196 problems (EN–VI) Question 45
Math Olympiad Vault · MathNet 2022-part-06 — 196 problems (EN–VI)