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February 28, 2020

GCD and Bezout Theorem

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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

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