MathDB

3

Part of 2023 Puerto Rico Team Selection Test

Problems(2)

2023 numbers from {-1,0,12} Puerto Rico TST 2023.1.3

Source:

3/23/2024
You have a list of 20232023 numbers, where each one can be −1-1, 00, 11 or 22. The sum of all numbers is 1919 and the sum of their squares is 9999. What are the minimum and maximum values of the sum of the cubes of those 20232023 numbers?
combinatoricsalgebra
p(2023) =? if p(k) =1/(k+1)

Source: Puerto Rico TST 2023.2.3

3/24/2024
Let p(x)p(x) be a polynomial of degree 20222022 such that: p(k)=1k+1   for    k=0,1,...,2022p(k) =\frac{1}{k+1}\,\,\, \text{for }\,\,\, k = 0, 1, . . . , 2022 Find p(2023)p(2023).
algebrapolynomial