﻿ Hanf Competition

## 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.

### 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 2n+1 and 2n-1 are both prime numbers.

Have fun solving the problems: