Number Theory Ln SolutionWe do this using Euclid Algorithm 2

Number Theory

Solution

We do this using Euclid Algorithm

25=11*2+3 , 3=25-2*11

11=3*3+2    , 2=11-3*3 =11*7-3*25

3=2+1            , 1=3-2=4*25-11*9

1=4*25-11*9

HEnce, 1=-11*9 mod 25

So, -9=25-9=16 is inverse of 11 mod 25

25=23+2              , 2=25-23

23=2*11+1          , 1=23-2*11=23*12-11*25

Hence,

1=23*12-11*25

So, 1=23*12 mod 25

So, 12 is inverse of 23 mod 25