At least how many residents of the country have the same birthday?

Question

I am trying to solve a pigeonhole question in discrete mathematics.

Let's suppose that a country has 11.000.000 people. At least how many residents of the country have the same birthday?

Take into consideration that leap years exist.

What I did is:

Let's suppose we have 2021. I take $\frac{10.000.000 \cdot 2021}{11.000.000} =1838$.

I believe I am wrong.

Answer 1

Just to give an answer for completeness based on lulu's comments:

There are $366$ possible birthdays and $\frac{11,000,000}{366}\approx 30054.6$

If each day had at most $30054$ people with that day as their birthday, then you would have at most $30054 \times 366 = 10,969,710$ people in total.

But there are more people than that, so you must have a day with at least $30055$ people with that day as their birthday.