International Mathematical Olympiad

In my entry on Gregory Perelman, I mentioned that he got a perfect score in the International Mathematical Olympiad, a contest for high-school math students. This contest features problems that, though they do not require knowledge of higher mathematics, are considered to be very difficult to solve. I thought some of my readers might like to see a sample problem.

Since it is difficult to use true mathematical notation in this format, I will use “**” to indicate exponentiation or, as some like to call it, raising to a power. For example, three squared is nine, and would be indicated as follows: 3**2. Okay then, here’s the problem.

Determine all pairs of integers X and Y, such that: 1 + 2**X + 2**(X+1) = Y**2.

It’s simply stated, is it not? Well, you’re welcome to try your hand at it. I don’t know what the solution is.