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## Get motivated

Consider the equation 2019x + 2020y = 2018. Are there integers x and y that satisfy this equation?

*Concepts in this lesson will help you to answer this question and more.*

## Concept – GCD, Bezout Theorem

GCD of two numbers a and b is their greatest common divisor. For example for 10 and 15, GCD is 5.

Bezout Theorem, in essence, describes the equation 10x + 15y = 5. It ensures that there are integer solutions to this equation. In fact for any two integers a and b, if GCD(a, b) = d, Bezout Theorem says that there are integer solutions to the equation: **ax + by = d**

## Watch Part 1

## Other useful links:-

- https://www.cheenta.com/complex-number-isi-entrance-b-stat-hons-2003-problem-5/
- https://www.youtube.com/watch?v=P4ZYA4XCQoM&list=PLTDTcDkWcXuxeaAMvWpx4vGIul38dKOQp&index=4