1. Find all solutions to the following linear congruences using
Fermat’s Little Theorem or Euler’s Theorem to help you. Show all
your steps.
(a) 3462x ≡ 6 173 (mod 59)
(b) 27145x ≡ 1 (mod 42)
1. Find the multiplicative inverse of 14 in GF(31) domain using
Fermat’s little theorem. Show your work.
2 Using Euler’s theorem to find the following exponential: 4200
mod 27. Show how you have employed Euler’s theorem here.
Q4. Find the multiplicative inverse of 14 in GF(31) domain using
Fermat’s little theorem. Show your work
Q5. Using Euler’s theorem to find the following exponential:
4200mod 27. Show how you have employed Euler’s theorem here
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)
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 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〉...
Consider a sample with six observations of 13, 13, 7, 23, 20,
and 20. Compute the z-score for each observation. (Leave no cells
blank - be certain to enter "0" wherever required. Round your
answers to 2 decimal places. Negative values should be indicated by
a minus sign.)