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Cover Letter for the 3 Lines Way Manuscript Taha M. Muhammad Goodlettsville, TN, USA August 4, 2026 Editorial Board Target Journal Name Subject: Submission of Manuscript – "Fermat's Last Theorem Proof (3 lines Way)" Dear Editor, I am writing to formally submit my manuscript, "Fermat's Last Theorem Proof (3 lines Way)", for consideration for publication as an independent research article. As an independent researcher who earned my Master’s degree in mathematics from the University of North Dakota on December 20, 1995, I have spent decades investigating structural frameworks and mathematical parameter reductions. My determination to pursue academic truth began in early childhood in Iraq, where I walked miles on dirt roads to seek permission to attend school—a lifelong journey of resilience that I have chronicled in my published memoir, We Survived Iraq and Turkey: Long Road to Freedom. While historical attempts and modern proofs of Fermat's Last Theorem rely on complex, high-dimensional modularity curves and elliptic curves, this paper offers an alternative perspective by condensing the algebraic problem into an ultra-short, 3-line structural proof framework. By embedding specific integer markdown offsets (u, v) and residual gap parameters (k, g) into a hypothetical target exponent baseline, the proof structures the exponential components to isolate core variances. The resulting balancing identities demonstrate that cumulative expansion changes prevent direct integer power matching, establishing a direct non-equality boundary for all exponents’ n > 2. Given the enduring historical and academic interest in concise, alternative methodologies for Diophantine equations, I believe this structured approach will offer unique insights to your readership. Thank you for your time, consideration, and fair evaluation of independent mathematical voices. I confirm that this manuscript is original, has not been published elsewhere, and is not currently under review by any other journal. Sincerely, Taha M. Muhammad Independent Researcher
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