Problems: Fall 2004
- Proof: Prove that there are infinite primes.
- What is the (Tau function) Τ(1000000).
- What is the (Euler function) Φ(1000).
- If m = 2004! (factorial), how many trailing zero's does m have.
- Prove that if the sum of the digits of a number is divisible by
3 than the number is divisible by 3. Then show what are the
conditions for divisibility by 11 and then prove it.
- Find the dimension of the Serspinsky Triangle.
Problems: Spring 2005
If M and N are the
coefficients such that (x^2)+ 1 is a factor of (5x^4) + (4x^3) +
(3x^2) + Mx + N, find the product of M and N.
numbers are chosen such that when each of the numbers is added to
the average of the other two, the results are 65, 69, and 69
respectively. Find the average of the original three numbers.
Let A be one of a
regular hexagon whose side length is one meter. To the nearest
centimeter, what is the sum of the distances from A to the other
five vertices of the hexagon?