MathDB

4

Part of 2021 AIME Problems

Problems(2)

2021 AIME I/4

Source: 2021 AIME I/4

3/11/2021
Find the number of ways 6666 identical coins can be separated into three nonempty piles so that there are fewer coins in the first pile than in the second pile and fewer coins in the second pile than in the third pile.
AMCAIME
It's not like I share a root with you or anything, baka!

Source: 2021 AIME II #4

3/19/2021
There are real numbers a,b,c,a, b, c, and dd such that −20-20 is a root of x3+ax+bx^3 + ax + b and −21-21 is a root of x3+cx2+d.x^3 + cx^2 + d. These two polynomials share a complex root m+n⋅i,m + \sqrt{n} \cdot i, where mm and nn are positive integers and i=−1.i = \sqrt{-1}. Find m+n.m+n.
AMCAIMEAIME II