MathDB

4

Part of 2017 Danube Mathematical Olympiad

Problems(2)

Diophantine Equation

Source: Mathematical Danube Competition 2017, Juniors P4

4/21/2022
Determine all triples of positive integers (x,y,z)(x,y,z) such that x4+y4=2z2x^4+y^4 =2z^2 and xx and yy are relatively prime.
number theoryDiophantine equationromania
Problem 4

Source: Danube Mathematical Competition 2017, Romania

10/28/2017
Let us have an infinite grid of unit squares. We write in every unit square a real number, such that the absolute value of the sum of the numbers from any n∗nn*n square is less or equal than 11. Prove that the absolute value of the sum of the numbers from any m∗nm*n rectangular is less or equal than 44.
combinatoricsabstract algebraabsolute value