Math 173A
Quiz #5 Solution
11/10/2011
Use the Chinese Remainder Theorem to solve the following system of linear
congruences. Write your solution as the least non-negative entry in its congruence
class. Carefully show work. (10 pts.)
x 3 mod 4
x 2 mod 7
x
Math 173A
Quiz #2 Solution
10/13/2011
1. (3pts) Exactly how many bit operations are needed to calculate the product 1011 101 ?
Blue digits are the result of a bit operation; there are 4 bit operations.
(3 pts.) correct.
1 0 1 (2 pts.): failed to left pad
Math 173A
Quiz #4 Solution
11/3/2011
Find all noncongruent solutions of the congruences below. Express solutions as the
least non-negative representative in the congruence class. Show work.
1. (3 pts.) 6 x 2
mod 9
gcd (6, 9) 3 , and 3 2 so there are no
Math 173A
Quiz #3 Solution
10/27/2011
1. (6 pts.) Use the Euclidian Algorithm to write the greatest common divisor of 371 and 71 as
a linear combination of 371 and 71, using integer coefficients.
371 71 5 16
71
16
16 4 7
7 2 2
7
2
3 1
1
Reversing:
1