I am trying to find the x $$113x\equiv 311 \mod 653$$ but using Euclidean algorithm I calculate until here $$(-152)(113)\equiv 1 \mod 653$$
This negative number is confusing me. How can I go further to find the inverse?
Or how can I change $$x\equiv -152 \mod 653$$ so that there wouldn't be any negative number?
Can I simplify the question using Chinese remainder theorem?
Wednesday 27 February 2013
congruences - Modular inverse question
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