SMRP is a 5 week summer program designed to give selected students the opportunity to work together with Willamette mathematics faculty members on a math research project. Students are awarded a $2000 stipend and room and board in the Haseldorf Apartments. Student participants will share the results of their research at the Student Scholarship Recognition Day (SSRD) on the Willamette Campus in the following April and the is a possibility of funding for students to present at a regional or national math conference.
The past two years we have studied a problem related to the Frobenius problem. The Frobenius problem (also known as the postage stamp problem) is described as follows.
Let A and B be relatively prime positive integers (think of these as stamp amounts). Find the positive integers (postage amounts) that cannot be made as a sum of the integers A and B? In particular, what is the largest such positive integer?
This largest such integer is called the Frobenius number of the set {A, B}.
An example: Let A=4 and B=5. The the postage amounts that cannot be made with these stamp amounts are:
1, 2, 3, 6, 7, and 11. The number 11 is the largest such number so the Frobenius number of {4, 5} is 11.