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math.GM2026
From Vieta to Chebyshev: A Unified Trigonometric Census of Polynomial Roots
Sawon Pratiher
This article gives a trigonometric method for counting how many roots of a polynomial are real and how many are complex, without solving the equation. For a depressed polynomial $P…
math.GM2016★ 1 cited
Recurrence Structures, Finite State Decomposition, and Statistical Bias in Collatz Path Sequences
Sawon Pratiher
We investigate the structure of Collatz path sequences for positive integers , where denotes the standard Collatz map. By classifying natural num…