👉 Wilson's Math, named after John Wilson, is a fascinating number theory result that connects prime numbers with divisibility properties. It states that for any natural number \( n \), the product of all integers from 1 to \( n-1\) (i.e., \( (n-1)! \)) is congruent to \(-1\) modulo \( n \) if and only if \( n \) is a prime number. Mathematically, this is expressed as \( (n-1)! \equiv -1 \mod n \) for prime \( n \). This theorem not only provides a criterion to test for primality but also reveals a deep symmetry in the factorial of numbers, linking combinatorial properties with number theory. It's a beautiful example of how simple products can encode profound mathematical truths.
