Are there any equations that look very hard to solve at first (e.g. many involved parameters etc), but can be solved/reduced efficiently solved with a certain algorithm? I'd like to create some programming problems/puzzles - hence the question.
I had the following ideas:
Given some integer and an equation, find a solution. The idea is that the problem should quickly explode in a computationally large problem, but can be solved very efficiently with some algorithm/trick.
Can anyone suggest some problems that could fit here? Maybe some diophantine equation problem, or something similar?