MathDB

BMT 2022 Guts #26

Source:

August 31, 2023

number theory

Problem Statement

Compute the number of positive integers

n

less than

10^8

such that at least two of the last five digits of

\lfloor 1000\sqrt{25n^2 + \frac{50}{9}n + 2022}\rfloor

are

6

. If your submitted estimate is a positive number

E

and the true value is

A

, then your score is given by

\max \left(0, \left\lfloor 25 \min \left( \frac{E}{A}, \frac{A}{E}\right)^7\right\rfloor \right)

.

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