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Dirichlet theorem in number theory
Problems related to number theory vary from divisibility to simple calculation. I will give a simple example that requires no complexity:
Given a 2024-regular polygon. On each vertice, a student numbers each vertice randomly from `1011. Prove that there exists a rectangular ABCD inscribed in the polygon so that: a+b=c+d where a,b,c,d are values of the vertices A, B, C, and D respectively.
There are also some problems that use divisibility as I’ve mentioned:
We are given 30 positive integers that have a sum of less or equal to 45. Prove that there exists a series of consecutive integers in those 30 integers that have a sum equal to 14:
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