# CofC Math Student Solves Math Horizons Problem

By | January 21, 2014

Lauren Tubbs, a junior Mathematics Major at the College of Charleston, recently worked on solving a multi-part problem that was posed in the Playground section of the September 2013 issue of Math Horizons, a journal published by the Mathematical Association of America.  Lauren successfully solved Problem 295 on “Counting Divisors” and submitted her solution to the journal.  The problem statement is:

(a) Show that, if n is an odd number, then n^2+19 has at least six divisors, and that n^2+119 has at least eight divisors.
(b) Are 19 and 119 the best possible numbers we could have chosen for part a?  For this part, (still assuming n is an odd number), find the smallest positive integers a and b such that n^2+a has at least six divisors, and n^2+b has at least eight divisors.

Lauren’s solution is here for anyone who would like to read it.  A common challenge for undergraduate math students is simply: How do I get started on mathematical research?  Professor Dinesh Sarvate, who has directed many undergraduate research projects here at CofC, describes one way to get students started:

In general,  when a student approaches me for research or when I see that a student is  capable of some research,  I ask them to do such problems from Math Horizons, the American Mathematical Monthly, or the College Mathematics Journal before giving a more time consuming research problem. So I hope to get students involved for years to come.

Lauren describes her experience in getting started below: