MathDB

1

Part of 2022 Thailand TSTST

Problems(3)

p^2022|n^2022+2022

Source: Thailand TSTST 2021, test 1, P1

8/16/2022
An odd prime pp is called a prime of the year 20222022 if there is a positive integer nn such that p2022p^{2022} divides n2022+2022n^{2022}+2022. Show that there are infinitely many primes of the year 20222022.
number theory
Polynomial equation

Source: Thailand TSTST 2021, test 3, P1

8/16/2022
Find all polynomials f,g,hf, g, h with real coefficients, such that f(x)2+(x+1)g(x)2=(x3+x)h(x)2f(x)^2+(x+1)g(x)^2=(x^3+x)h(x)^2
algebra
ok combi

Source: 2021 Thailand October Camp 4.1

5/6/2023
Let n≥3n\geq 3 be an integer. Each vertex of a regular nn-gon is labelled with a real number not exceeding 11. For real numbers a,b,ca,b,c on any three consecutive vertices which are arranged clockwise in such an order, we have c=∣a−b∣c=|a-b|. Determine the maximum value of the sum of all numbers in terms of nn.
combinatorics