amnakhan786 Posted November 19, 2012 Share Posted November 19, 2012 I am a beginner in modular arithmetic area, and i am studying modular arithmetic. i came across a question, if i have mod 5 or mod 7, since they are smaller numbers it is easier to find their multiplicative inverse as they are prime, but anything that is even for example , i couldnt understand the following practice problem: 106x (is congruent to) 10 mod 284 As far as i understand the multiplicative inverse exists if gcd(106,284)=1, since 284 is not prime, since gcd(106, 284 mod 106) = gcd(106,72)= gcd(72,106)= gcd(34,72)=gcd(4,34)=gcd(2,4)=gcd(0,2) hence gcd of (106,284)=2. 1) but how do i know for sure that the multiplicative inverse doesnot exist for this qs. Can i somehow prove it. 2) what if 284 is replaced by 283? Link to comment Share on other sites More sharing options...
Recommended Posts