The Divine Calculus: Algebra and Diophantine Equations in The Holy Quran

The structural, linguistic, and mathematical frameworks included in the Holy Quran are investigated in this research, especially how its textual design corresponds with fundamental algebraic ideas and Diophantine equations. The Quranic book has an exact numerical pattern that have historically been recognized as the engine behind the Golden Age of Islamic mathematics, which directly influenced Al-Khwarizmi's formulation of Al-Jabr. This study investigates the mathematical basis of Islamic inheritance law (ilm al-fara'id) as a system of linear equations, investigates the structural symmetries of word frequencies as discrete algebraic balancing, and models particular alphanumeric systems (Abjad) using indeterminate analysis and Diophantine equations  The article shows how the Quranic text links linguistic revelation with exact mathematical design by means of an analysis of these frameworks, hence presenting a divine viewpoint on cosmic and scriptural equilibrium.