The "fun litle puzzle" was a nightmare to me when I first came across it, which was on the 1971 Putnam exam. I spent a lot of time trying to solve it by doing $2^x,3^x$. When Serge Lang told me after the test that $2^x,3^x$ was a notorious open problem, I didn't know whether to be pleased that my intuition had led me to something widely held to be true, or annoyed that I had spent so much precious exam time on an approach that was doomed.
The "fun litle puzzle" was a nightmare to me when I first came across it, which was on the 1971 Putnam exam. I spent a lot of time trying to solve it by doing $2^x,3^x$. When Serge Lang told me after the test that $2^x,3^x$ was a notorious open problem, I didn't know whether to be pleased that my intuition had led me to something widely held to be true, or annoyed that I had spent so much precious exam time on an approach that was doomed.