👉 Kruger's Math, also known as the "Kruger's Number Theory," is a fascinating area of mathematics that explores the surprising and often counterintuitive properties of numbers, particularly in modular arithmetic. It reveals that many properties we intuitively expect from arithmetic to hold universally do not always apply, especially when considering numbers modulo a prime or a power of a prime. For instance, while it's often assumed that if \(a \equiv b \pmod{n}\), then \(a^k \equiv b^k \pmod{n}\) for any integer \(k\), Kruger's Math shows this is not always true. This phenomenon, known as "non-uniqueness of solutions" in modular arithmetic, challenges our basic understanding and has profound implications in number theory, cryptography, and computer science. It highlights the complexity and richness of number systems beyond our everyday experiences with integers.
