MASC 380 Assignment #2

Due 21 October, 1998.

1. It's very easy to tell whether an integer written in base 10 is divisible by 2 or not: just check whether the last digit is even or odd. Thus 12, 50360, and 1234 are divisible by 2 since 2, 0, and 4, respectively, are even. On the other hand, 11, 367, and 12345 are not divisible by 2, since 1, 7, and 5, respectively, are odd. It's not quite so easy to tell whether an integer is divisible by 3 or not, but the following trick does make it much easier.

The ``Rule of Three''

An integer is divisible by 3 if and only if the sum of its digits is divisible by 3.

For example, to test whether 12345 is divisible by 3 or not, we need only check whether 1 + 2 + 3 + 4 + 5 = 15 is divisible by 3 or not. (Note that we could, in turn, check whether 15 is divisible by 3 by checking whether 1 + 5 = 6 is divisible by 3.)

Your mission is to figure out for which b and k a ``Rule of k'' works in base b. (Preferably with some reasons why...) [5]

2. Find out what you can about the life of Thales of Miletus (start with Chapter 6 of the text), and our sources of information about him. How reliable, in your opinion, is the data, especially that about his education and his work? Why? [5]

Please be nice to your fellow classmates and do not take any relevant books out of Bata Library. Replace them on the shelves, exactly where you found them!

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