Lennox's Theorem

Lennox's Theorem relates to a specific type of polynomial equation called cyclotomic polynomials, which are involved in constructing roots of unity—complex numbers that, when raised to a certain power, equal 1. The theorem provides criteria for when these polynomials are reducible or irreducible over the rational numbers, meaning whether they can be factored into simpler polynomials with rational coefficients. In essence, it helps mathematicians understand the fundamental building blocks of certain algebraic expressions involving roots of unity, shaping how we analyze and work with these special polynomials in number theory and algebra.