Question 45
For every positive integer $n$, define
$$
V_n=\left\lfloor2^n\sqrt{2020}\right\rfloor+\left\lfloor2^n\sqrt{2021}\right\rfloor.
$$
Prove that the sequence $V_1,V_2,\ldots$ contains infinitely many odd integers and infinitely many even integers.
Here $\lfloor x\rfloor$ denotes the largest integer not exceeding $x$.
$$
V_n=\left\lfloor2^n\sqrt{2020}\right\rfloor+\left\lfloor2^n\sqrt{2021}\right\rfloor.
$$
Prove that the sequence $V_1,V_2,\ldots$ contains infinitely many odd integers and infinitely many even integers.
Here $\lfloor x\rfloor$ denotes the largest integer not exceeding $x$.