Search for a tool
Bezout's Identity

Tool to compute Bezout coefficients. The Bezout Identity proves that it exists solutions to the equation a.u + b.v = PGCD(a,b).

Results

Bezout's Identity -

Tag(s) : Arithmetics

Share
Share
dCode and more

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!


Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!


Thanks to your feedback and relevant comments, dCode has developed the best 'Bezout's Identity' tool, so feel free to write! Thank you!

Bezout's Identity

Sponsored ads

Bezout Identity Calculator



Answers to Questions (FAQ)

What is Bezout Identity?

The Bachet-Bezout identity is defined as : if $ a $ and $ b $ are two integers and $ d $ is their GCD (greatest common divisor), then it exists $ u $ and $ v $, two integers such as $ au + bv = d $.

Example: $ a=12 $ and $ b=30 $, gcd $ (12, 30) = 6 $. There are multiple solutions to $ u $ and $ v $ such as $ 12u + 30v = 6 $, such as : $$ 12 \times -2 + 30 \times 1 = 6 $$

The dCode Bezout coefficients calculator gives only one solution.

What are Bezout coefficients?

The Bézouts coefficients are the values $ u $ and $ v $.

How to calculate values for Bézout Identity?

The dCode program uses the extended GCD algorithm. $ a $ and $ b $ are two non-zero positive integers.

The algorithm of dCode consists of a sequence of Euclidean divisions for finding the Bezout coefficients (and also the GCD).

How to code Bézout Identity in pseudo-code?

A source code for the identity of Bezout would be similar to this pseudo-code:

Initialization r = a, r' = b, u = 1, v = 0, u' = 0 and v' = 1
While (r' != 0)
q = (int) r/r'
rs = r, us = u, vs = v,
r = r', u = u', v = v',
r' = rs - q*r', u' = us - q*u', v' = vs - q*v'
End While
Return (r, u, v)

Source code

dCode retains ownership of the online 'Bezout's Identity' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any 'Bezout's Identity' algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any 'Bezout's Identity' function (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and no data download, script, copy-paste, or API access for 'Bezout's Identity' will be for free, same for offline use on PC, tablet, iPhone or Android ! dCode is free and online.

Need Help ?

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

Questions / Comments

Thanks to your feedback and relevant comments, dCode has developed the best 'Bezout's Identity' tool, so feel free to write! Thank you!


Source : https://www.dcode.fr/bezout-identity
© 2021 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.
Feedback