Algorithm | 代写math – MATH/CSCI 4116


Algorithm | 代写math – 该题目是一个常规的math 的练习题目代写, 包括了math 等方面, 这个项目是assignment代写的代写题目

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 assignment 8
  1. (a) Use the Euclidean Algorithm to compute gcd(239,124).

(b) Use your calculations above (that is, use the extended Euclidean algorithm) to represent the gcd as a linear combination of 239 and 124.

  1. (a) Find integersxandy such that 17x+ 101y= 1.

(b) Use the result in (a) to find 17^1 (mod 101).

  1. Question 2 indicates how the extended Euclidean algorithm can be used to determine modular inverses (if they exist). Use this to find (a) 357^1 (mod 1234); (b) 3123^1 (mod 9987).
  2. (a) Compute the subgroup generated by 2 + 17Zin (Z/ 17 Z).

(b) Compute the order of 2 (mod 1237).

(Hint: Use the results from Sect. 5.2 to decide which orders arepossible.)

  1. Determine the orders of all elements in (Z/ 15 Z).

Note: Only after Fridays class you will be able to do the following ques- tion.

  1. (a) Use Fermats little theorem to compute 2^122 (mod 13).

(b) Use Eulers theorem to find the last digit in the decimal representa- tion of 3^400.

Due: Thursday, March 23, 2023