compute 7^-1 mod 11? in details

compute 7^-1 mod 11?

in details

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 3 months ago

a) Use Fermat’s little theorem to compute 52003 mod 7, 52003 mod 11, and 52003 mod 13.

a) Use Fermat’s little theorem to compute 52003 mod 7,52003 mod 11, and 52003 mod 13. b) Use your results from part (a) and the Chinese remaindertheorem to find 52003 mod 1001. (Note that1001 = 7 ⋅ 11 ⋅ 13.)

Compute the following: (a) 13^2018 (mod 12) (b) 8^11111 (mod 9) (c) 7^256 (mod 11) (d)...

Compute the following: (a) 13^2018 (mod 12) (b) 8^11111 (mod 9) (c) 7^256 (mod 11) (d) 3^160 (mod 23)

Compute additive and multiplicative inverses of 7 and 9 in Z11 (mod 11). Find out whether...

Compute additive and multiplicative inverses of 7 and 9 in Z11 (mod 11). Find out whether or not 4 and 7 have multiplicative inverse in Z14 (mod 14). Let S be the set of even integers under the operations of addition and multiplication. Is S a ring? Is it commutative? Is it a field? Justify your answer. Compute the multiplicative inverse of 9 under modulo 31 using the extended Euclid’s algorithm.

Consider the curve y2 ≡ x3 + 4x + 7 mod 11 1. For a point...

Consider the curve y2 ≡ x3 + 4x + 7 mod 11 1. For a point P= (2,10), find 2P (or double) 2. For two of the points P = (2,1) and Q =(7,2), find P+Q 3. Find the bound for the number of points on this curve using Hesse’s theorem.

0 mod 35 = 〈0 mod 5, 0 mod 7〉 12 mod 35 = 〈2 mod...

0 mod 35 = 〈0 mod 5, 0 mod 7〉 12 mod 35 = 〈2 mod 5, 5 mod 7〉 24 mod 35 = 〈4 mod 5, 3 mod 7〉 1 mod 35 = 〈1 mod 5, 1 mod 7〉 13 mod 35 = 〈3 mod 5, 6 mod 7〉 25 mod 35 = 〈0 mod 5, 4 mod 7〉 2 mod 35 = 〈2 mod 5, 2 mod 7〉 14 mod 35 = 〈4 mod 5, 0 mod 7〉...

1. Use backward substitution to solve: x=8 (mod 11) x=3 (mod 19)

1. Use backward substitution to solve: x=8 (mod 11) x=3 (mod 19) 2. Fine the subgroup of Z24 (the operation is addition) generates by the element 20. 3. Find the order of the element 5 in (z/7z)

Using the following sample data; 6, 7, 11, 6, 11, 5, 15, 11, 5; Compute the...

Using the following sample data; 6, 7, 11, 6, 11, 5, 15, 11, 5; Compute the sample standard deviation using either the computing formula or the defining formula. A. 3.6 B. 3.5 C. 3.4 D. 3.3

Use the Extended Euclid's Algorithm to solve ƒ-1 for 8 mod 11

1. compute the least non-negative residue of 4^n (mod 9) for n=1,2,3,4,5.... prove that 6*(4^n)=6 (mod...

1. compute the least non-negative residue of 4^n (mod 9) for n=1,2,3,4,5.... prove that 6*(4^n)=6 (mod 9) for every n>0. 2. find nice tests for divisibility of numbers in base 34 by each of 2,3,5,7,11,and 17. 3. in Z/15Z, find all solutions of : (i) [36]X=[78]. (ii) [42]X=[57] (iii) [25]X=[36] 4. in Z/26Z, find the inverse of [9], [11], [17], and [22] 4. write the set of solutions of x=5 mod24. x=17 (mod 18) for all equation line, there are...

For m, n in Z, define m ~ n if m (mod 7) = n (mod...

For m, n in Z, define m ~ n if m (mod 7) = n (mod 7). a. Show that -341 ~ 3194; that is to say 341 is related to 3194 under (mod 7) operation. b. How many equivalence classes of Z are there under the relation ~? c. Pick any class of part (b) and list its first 4 elements. d. What is the pairwise intersection of the classes of part (b)? e. What is the union of...

Question