The Frobenius problem for triples (Spring 2020)

If you start with any two numbers p and q which share no common factor, then by taking nonnegative linear combinations of p and q you can make any sufficiently large number, in particular anything larger than pq-p-q. This is known as the Frobenius Problem or the Chicken McNugget Problem.

What happens if we take three numbers p, q, and r which collectively share no common factor? It is known that we can construct any sufficiently large number, but what "sufficiently large" should be is not known in general (the largest number which cannot be constructed is called the Frobenius number). We will look at the problem of finding the Frobenius number of triples for some special cases of numbers. We will also look for patterns in the sets of numbers which cannot be constructed.

(Technical description with more details.)

People

• Alexandra Beskau (Undergrad)

• Steve Butler (Faculty)

• Brittany Fredericks (Undergrad)

• Tiffany Geistkemper (Undergrad)

• Henry Klatt (Undergrad)

• Kate Lorenzen (Grad)

• Hayan Nam (PostDoc)

Pre-requisites

• Experience with proofs (Math 201 or Math 317)

• Experience with combinatorics (Math 304) is desirable, but not necessary

• Experience with programming (e.g. Python) is desirable, but not necessary