Create Bézout’s Identity (Extended Euclidean Algorithm) #1759
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Bézout’s Identity is a fundamental theorem in number theory that states: for any two integers 𝑎 a and 𝑏 b with a greatest common divisor 𝑑 d, there exist two integers 𝑥 x and 𝑦 y such that: 𝑎 𝑥 + 𝑏 𝑦 = 𝑑 ax+by=d The Extended Euclidean Algorithm is an extension of the Euclidean algorithm that not only finds the GCD of two integers 𝑎 a and 𝑏 b but also finds the coefficients 𝑥 x and 𝑦 y that satisfy Bézout's Identity. This algorithm has practical applications in: Solving linear Diophantine equations. Computing modular inverses (important in cryptography). Finding integer solutions in various number theory problems.
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can u tell me how do i add that ? |
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@ananyashinde2434 do you know how to operate git on vs code |
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do one thing open this https://github.com/ananyashinde2434/C and press Dot button . this will convert your github into VS code environment and you will be more comfortable to contribute. |
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But before that sync latest changes on you github by this |
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can u tell me where is the dot button u r talking about ? |
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dot button on keybord |
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Bézout’s Identity is a fundamental theorem in number theory that states: for any two integers 𝑎 and 𝑏 with a greatest common divisor
d, there exist two integers 𝑥 and 𝑦 such that:
𝑎𝑥+𝑏𝑦=𝑑 The Extended Euclidean Algorithm is an extension of the Euclidean algorithm that not only finds the GCD of two integers a and b but also finds the coefficients
𝑥 and y that satisfy Bézout's Identity. This algorithm has practical applications in:
Solving linear Diophantine equations.
Computing modular inverses (important in cryptography). Finding integer solutions in various number theory problems.