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
Names of animals and their numbers
The following table will be used in certain problems.
| Animal || Number
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!).
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
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
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
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:
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
84746 45152 36179
What animal's name is Bob sending to Alice?