👉 The Donald Math, also known as the Donald Problem or the Donald Problem of the Day, is a simple yet intriguing mathematical puzzle that challenges our intuition about the nature of numbers and their representations. It goes like this: given a positive integer \( n \), find the smallest positive integer \( m \) such that \( 10^m \equiv 1 \pmod{n} \). This integer \( m \) is called the order of 10 modulo \( n \). The problem is named after the mathematician Richard Donald, who popularized it in the 1980s. The key insight is that \( m \) must divide \( \phi(n) \), where \( \phi \) is Euler's totient function, which counts the integers up to \( n \) that are coprime to \( n \). The Donald Math is significant because it connects number theory, particularly modular arithmetic and group theory, with computational complexity, offering a rich area for exploration in both theoretical and applied mathematics.
