MathDB

4

Part of 2017 Thailand TSTST

Problems(3)

3mk=3(m+3)^n+1

Source: 2016 Thailand October Camp 1.4

2/26/2022
Suppose that m,n,km, n, k are positive integers satisfying 3mk=(m+3)n+1.3mk=(m+3)^n+1. Prove that kk is odd.
number theoryDiophantine equation
#22 functional equation

Source:

5/9/2021
Find all function f:N∗→N∗f:\mathbb{N}^*\rightarrow \mathbb{N}^* that satisfy: (f(1))3+(f(2))3+...+(f(n))3=(f(1)+f(2)+...+f(n))2(f(1))^3+(f(2))^3+...+(f(n))^3=(f(1)+f(2)+...+f(n))^2
functionfunctional equationalgebra
Color black/white in 8*8 table

Source: 2016 Thailland October Camp 3.4

2/28/2022
The cells of a 8×88 \times 8 table are colored either black or white so that each row has a different number of black squares, and each column has a different number of black squares. What is the maximum number of pairs of adjacent cells of different colors?
combinatoricsColoringcellstableconstruction