Mathematics
Solving Recurrence Relations Using Characteristic Equations
Quick fact
The characteristic equation method was popularized in the 18th century and is essentially the same technique used to solve linear differential equations—both rely on guessing exponential solutions.
Why this is interesting
You know the Fibonacci numbers: 0, 1, 1, 2, 3, 5, 8... each term is the sum of the previous two. But what if you need the 1000th term directly—without computing all 999 before it?