Math 459, Senior Seminar
10/4/11
Name: Grace DeTore
Title: Repeating Decimals
Source: W.G. Leavitt, The College Mathematics Journal, Mathematical Association of
America, 15, no. 4, (1984), pp299-308
Senior Project Ideas:
1.) Explore how Fermat’s Little Theorem plays a key role in encryption algorithms such
as the RSA (Rivest, Shamir and Adleman) scheme. The RSA scheme is based on the fact
that multiplying two primes is easy, whereas figuring out the prime factors of a
composite number is difficult. Explore how the this connects with encrypting and
decrypting codes between parties.
2.) Using Gauss’ method it is easy to find if x^2  a(modp) has a solution. But if there is
a solution, it can be hard to find if the number in question is large. In some cases it can
be as hard as factoring the large number. Does there exist certain “nice” qualities for a
number such that we (/computing system) can find a solution in reasonable time?
3.) Explore the rest of Leavitt’s “Repeating Decimals” to come to a more general solution
to our question of “does the decimal expansion of m/n have the nines property”.