Triangular numbers are those numbers that are the sum of an initial segment of the positive integers. Mersenne numbers are numbers that are $1$ less than an integer power of $2$. As number theorists will, it may be asked how many Mersenne numbers are triangular as well, and what exactly is the list of those numbers. Ramanujan made a conjecture about the list of solutions to a certain Diophantine equation, which was later proven by Nagell. Interestingly, we can manipulate this equation into a different form to find all triangular Mersenne numbers. That is the goal of this video.