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William P. Hanf Undergraduate Competition
Problem of the Month for Manoa Undergraduates

With our Problem of the Month for Manoa Undergraduates, we would like to stimulate mathematical discussion and competition amongst our undergraduate students. A modest cash award will be given to the winners from the William P. Hanf Memorial Fund.

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 following rules may be changed or clarified from month to month:

  1. Any regular undergraduate currently enrolled at UH Manoa is eligible to compete.
  2. Write a complete solution with all details to either problem or both.
  3. Submit your solution(s) by email before the end of the above month to Professor David Bleecker at

    bleecker@math.hawaii.edu

    For the subject line of your email use "problem of the month" and send your email via your UH email address. Either write your solution within the body of your email or within attachment(s) in the form of readable pdf files or images of your work in jpg format (e.g., scanned or digitally photographed).
  4. Solutions will be judged by a committee of professors according to a combination of criteria: accuracy, attention to details, chronological order of submission, and neatness, but not necessarily in that order.
  5. Before the end of the 10-th day of the month that follows, the winner(s) will be announced on the Math Department web site. Moreover, if there is at least one good answer to a problem the winner(s) for that problem will collectively receive a total of least $20 to be distributed among them depending on the criteria in 4 above, as soon as the checks can be extracted from the Hanf Fund at the UH Foundation, a process that may take several weeks.

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: