Thursday, 25 October 2018

number theory - Solving linear congruence (modular inverse or fraction) by solving Bezout equation

Isn't finding the inverse of a, that is, a in aa1(modm) equivalent to solving the diophantine equation aamb=1, where the unknowns are a and b? I have seem some answers on this site (where the extended Euclidean Algorithm is mentioned mainly) as well as looked up some books but there is no mention of this. Am I going wrong somewhere or is this a correct method of finding modular inverses? Also can't we find the Bézout's coefficients by solving the corresponding diophantine equation instead of using the extended Euclidean Algorithm?

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