MathDB

2

Part of ICMC 5

Problems(2)

Subtracting rows leaves all remainders

Source: ICMC 2022 Round 1 P2

12/4/2021
Find all integers nn for which there exists a table with nn rows, 20222022 columns, and integer entries, such that subtracting any two rows entry-wise leaves every remainder modulo 20222022.
Proposed by Tony Wang
tablecombinatoricsnumber theorycollege contestsICMC
just a sum

Source: 2022 ICMC Round 2 P2

3/1/2022
Evaluate 1/21+2+1/41+24+1/81+28+1/161+216+⋯\frac{1/2}{1+\sqrt2}+\frac{1/4}{1+\sqrt[4]2}+\frac{1/8}{1+\sqrt[8]2}+\frac{1/16}{1+\sqrt[16]2}+\cdots
Proposed by Ethan Tan
ICMCalgebraanalysiscalculuscollege contests