Saturday 22 August 2015

elementary number theory - What is a modular inverse?

I realize that this question has been asked before; please just bear with me. I looked across the Internet on here, Khan Academy, and many other sites in order to understand what an inverse mod is and how to calculate it.



The closest explanation I got is



enter image description here



However, I can't for the life of me figure out how we get the equation in the second bullet point. I tried testing it out in Python programming language by representing ^ as both xor and "to the power of" symbol ** (example for those who have not used it: 2 ** 4 = 16) and replacing mod with % (modulo).




To anyone who knows, please explain exactly what a modular inverse is and how to solve it.



As someone said, I should probably tell why I am saying "the" modular inverse. I came across this while doing Problem 451 of Project Euler and am trying to find greatest modular inverse (if I have function l(n) then the modular inverse I am calculating must be less than n-1)

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