## William P. Hanf Undergraduate Competition

for Manoa Undergraduates

With our *List of Problems*, we would like to
stimulate mathematical discussion and competition amongst our undergraduate students.

Fondly remembered UH math professor, William P. Hanf is known for his contributions to mathematical logic. While at UC Berkeley, he scored among the top five contestants in the Putnam Mathematical Competition in 1954, along with Benjamin Muckenhoupt (Harvard), James Daniel Bjorken (MIT), and Leonard Evens (Cornell), and Kenneth G. Wilson (Harvard) who went on to win the Nobel Prize in Physics in 1982. |

The competition is designed for all undergraduate students who have an interest in mathematics. Students considering future careers in mathematics or fields closely related to mathematics are especially encouraged to participate.

### Reasons for participating

### Rules of the competition

### Kudos

### Sample problem:

Recall that a positive integer p is a prime number if and only
if p > 1 and p has no positive integer divisors other than itself and 1.
Find all positive integers n such that 2^{n}+1 and 2^{n}-1 are both prime
numbers.

Have fun solving the problems: