compute 7^-1 mod 11? in details

compute 7^-1 mod 11?

in details

Solutions

Expert Solution

The solution of this question is based upon Extended Euclidean Algorithm, we use it to find the multiplicative inverse of the number a

The first condition is that in a(mod b) variable 'a' and 'b' must be co primes.

Now we need to use this algorithm to find gcd of 'a' and 'b' and also find 'x' and 'y'. Such that

ax + by = gcd(a,b)

To find multiplicative inverse Of 'a' under 'm' Put b = m. Since a and m are relatively prime so gcd = 1.

=> ax + by = 1

Take modolu m on both sides

ax + my = 1(mod m)

my mod m value is always 0

ax = 1 ( mod m )

Here, x is the multiplicative inverse of 'a'.

so, value of 7^-1(mod 11) is 8.

venereology answered 1 month ago

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