# Homework for the math lectures at the 2002 Governor's School

We should have some homework. I can get some evidence to help me judge how I am doing, and you can show me how clever you are!

## Names of animals and their numbers

The following table will be used in certain problems.

Animal Number
Elephant 9
Frog 13
Banana 5
Heron 128
Bicycle 2003

### Explain

Please give explanations of your answers. This could be sentences such as "I used the Maple instruction Priming(203); and the answer Maple gave contained the following information which ..." Unsupported answers are not useful for students (or teachers!).

### Cooperate ...

You may work together in groups of no more than 5. You may give me homework solutions to be credited to a group of students. Please write clearly and indentify everyone carefully. Everyone whose name appears on a solution should understand the work that was done.
 Hints I may give hints by e-mail if you need a hint & if I read the message & if I have the time.
Due at the start
of class on
Suggested problems
REVISED
Thursday, July 11

1. What are the first 5 decimal digits of 2300? What are the last 5 decimal digits of 2300?

2. How many decimal digits does 2(2(2 (22))) have? What about (((22)2)2) 2)? (I think the first number is the largest you can get with five 2's and exponentiation and parenthesizing and the second is the smallest.)

3. Here is a secret-sharing example mod 17. Find the constant term mod 17 of a fourth degree polynomial P so that

P(1)=2   P(2)=4   P(3)=6   P(4)=8   P(10)=15
The number should identify one of the animals in the table above.
Comment Do all computations mod 17. Maple is "smart" enough. This will reduce the work needed.

4. Alice and Bob are using RSA. They agree on the following modulus which is the product of two primes:

3  29220   27360   43431   10697
Alice's public key is
349  16502  12311
and Bob encrypts the number of an animal (from the table above) using her public key: he sends
84746  45152  36179  77517
What animal's name is Bob sending to Alice?