Anirudh Vegesana contributed to the leanprover-community/mathlib4 repository by formalizing a new theorem in ring theory, proving that exp(n) minus one is nilpotent for any nilpotent element n. This work deepened the algebraic foundations of mathlib4, providing a more robust framework for future extensions and optimizations in formal mathematics. Using Lean and leveraging skills in formal verification and theorem proving, Anirudh implemented and documented the proof with clear commit messages and explicit co-authorship. The contribution reinforced the reliability of core algebraic reasoning in the library, supporting safer downstream tools and enabling more dependable mathematical results for the community.