First, props are due to my friend Natalie Jackucyn of Chicago for introducing me to a variation on this problem a few years ago. I pitched this version of the problem to my Precalculus class this week as a way to review some of their Algebra II topics while enhancing their problem-solving ideas and learning how to use their new CAS handhelds. Here’s the problem:
One of the terms in the expansion of is . If A, B, and n are all integers, what are their values?
For me, the process is critically important. The answers don’t really matter; they just happen. I’ll post my students’ ideas in a few days, but for now I leave it open to any readers to leave their thoughts.