Question

Find an inverse of 4 modulo 13

Answer #1

Find the inverse of 1234 modulo 2345

We say that x is the inverse of a, modulo n, if ax is congruent
to 1 (mod n). Use this definition to find the inverse, modulo 13,
of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
Show by example that when the modulus
is composite, that not every number has an inverse.

Find the least positive inverse for 83 modulo 660.

a. Show that if a has a multiplicative inverse modulo N,then
this inverse is unique (modulo N).
b. How many integers modulo 113 have inverses? (Note: 113 =
1331.)
c. Show that if a ≡ b (mod N) and if M divides N then a ≡b (mod
M).

Use extended Euclid algorithm to find the multiplicative inverse
of 27 modulo n, if it exists, for n = 1033 and 1035. Show the
details of computations.

In GF(24), derive the multiplicative
inverse of x2 modulo
(x4+x+1).

Using Fermat’s Little theorem, find the multiplicative inverse
of 4 in mod 13. Show your work.
Using Euler’s theorem, find 343 mod 11.

Given that 2 is a primitive root modulo 19, find all the
primitive roots modulo, 19. You must know how you are getting your
answer and make sure all your answers are in the canonical residue
set

4. Find the inverse function of f. State the domain and range
(in interval notation) of the
inverse function f exponent of −1 (x).
f(x) = 4 + 5x all over 3x − 6

Find the inverse laplace of s/[(s+2)(s^2+4)]

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