UMBC CMSC203 Discrete Structures, Section 06, Spring 2016
Homework 6, Due Thursday, 03/10
Arithmetic with mod. Use the repeated squaring technique
to compute 26^{37} % 77. Show all of your work. Your work
should not have any numbers bigger than 77^{2} = 5929.
Inverses mod 23. For each integer x,
1 ≤ x < 23, find an integer y,
1 ≤ y < 23, such that
x ⋅ y ≡ 1 (mod 23).
In other words, x ⋅ y % 23 = 1.
Then, x and y are called inverses modulo 23.
GCD Proof.
Let a and b be integers such that a is even
and b is odd. Argue that gcd(a, b) =
gcd(a/2, b).
Euclid's Algorithm.
Use Euclid's algorithm to compute gcd(18893511, 1154300). Show all of your work.
Extended Euclid's Algorithm.
Use the Extended Euclid's Algorithm to find the multiplicative inverse of
173 modulo 235012. Show all of your work.