Möbius Inversion
Möbius Inversion is a mathematical technique used in number theory and combinatorics. It allows one to invert summation formulas involving arithmetic functions. Essentially, if you have a function that sums values over divisors, Möbius inversion helps you express the original function in terms of its summatory function.
The method relies on the Möbius function, which assigns values based on the prime factorization of integers. By applying the Möbius function, you can transform sums of functions into a different form, revealing deeper relationships between numbers and their divisors. This technique is particularly useful in solving problems related to counting and partitioning.