2021 AMC 12B Problems/Problem 15

Revision as of 14:23, 29 September 2020 by Icematrix2 (talk | contribs) (Created page with "{{duplicate|2021 AMC 12B #15 and 2021 AMC 10B #20}} ==Problem== The number <math>2021</math> is expressed in the form <cmat...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
The following problem is from both the 2021 AMC 12B #15 and 2021 AMC 10B #20, so both problems redirect to this page.

Problem

The number $2021$ is expressed in the form \[2021=\frac{a_1!a_2!...a_m!}{b_1!b_2!...b_n!},\] where $a_1 \geq a_2 \geq \cdots \geq a_m$ and $b_1 \geq b_2 \geq \cdots \geq b_n$ are positive integers and $a_1+b_1$ is as small as possible. What is $|a_1 - b_1|$? $\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 5$

Invalid username
Login to AoPS