Thursday, 10 August 2017

number theory - Can the extended euclidean algorithm be used to calculate a multiplicative inverse in this case?

e=503456131 is a prime number. It is relatively prime to the number b=10000123400257488



If I use the extended euclidean algorithm (using this python implementation) to calculate the coefficients on the linear combination of e and b that gives 1, I obtain 906226286492069e+45623955b=1.




Is it not correct that the coefficient on e, namely 906226286492069, is a multiplicative inverse of e (mod b)?



I thought this was correct, but 906226286492069e divided by b gives remainder 10000096.



What am I not seeing here?

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