1. Discrete Math for CS CMPSC 360 LECTURE 13 Last time:
Modular arithmetic
Exponentiation
Multiplicative Inverses
Extended Euclid’s algorithm
Today:
Chinese remainder theorem
CMPSC
360
12/28/2018

2. I-clicker problem (frequency: BC)
Compute 𝑚𝑜𝑑 50.
Answer: 7.
42.
43.
49.
51.
12/28/2018

3. I-clicker problem (frequency: BC)
The multiplicative inverse of 7 𝑚𝑜𝑑 50 is 7.
42.
43.
49.
It does not exist.
12/28/2018

4. Old woman riddle Old women goes to a market with a basket of eggs.
A horse accidentally steps on her basket, crushing all the eggs. The rider offers to pay for her damage and asks how many eggs she has.
When she had take out 3 at a time, there were 2 left.
When she took them 5 at a time, there were 3 left.
When she took them 7 at a time, there were 2 left.
What’s the smallest number of eggs she could have had?
12/28/2018