HMMT 2007 U24

Let $x, y, n$ be positive integers with $n>1$ . How many ordered triples $(x, y, n)$ of solutions are there to the equation $x^{n}-y^{n}=2^{100}$ ?

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.