Solving a Math Olympiad Question | Solving a System of Equations Equation For Integer Solutions

🔴 Solving a Math Olympiad Question | Solving a System of Equations Equation For Integer Solutions | A Math Olympiad Problem With Integer Solutions

Hey there.

In this video, we want to solve another math olympiad question, in which we have a system of equations with integer solutions. We are given
xy+z=2020
and
x+yz=2021
and x, y, and z are integers, and we want to solve for them.
To do that, we should try to manipulate the given equations and try to factor out some terms to be able to solve for integer solutions.
one of the most important things is that 2021-2020 is 1.

🔴I hope you enjoy watching this video.🔴

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topics covered in this video:
solving a math olympiad question
solving a system of equations with integer solutions
solving a diophantine equation
2021 math olympiad problem

#solveForIntegers #matholympiad #DiophantineEquation #MathOlympics

[Johnny-cjuf]

If we look for other real solutions and if I'm not mistaken, there are an infinite of possible combinations for the system to work: we have (x-z)(1-y)=1, so we deduce that it is enough for (x-z) and (1-y) to be inverse for the equation to be verified, we have for example x=1348, z=1346 and y=(1/2) and many others... :)
Nice video !