Abstract
Chebyshev and his students Zolotarëv, the brothers V. A. and A. A. Markov, Korkin, and Posse reduced extremal problems for polynomials to Pell’s equation, a geometric interpretation of which is suggested in the following construction.
Essentially, all the quantities in this (Abel-Pell) equation are unknown, even the degree of the polynomial. Nonetheless it is possible to solve it!
M. Sodin and P. Yuditskii [139]
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Bogatyrev, A. (2012). Chebyshev Representation of Polynomials. In: Extremal Polynomials and Riemann Surfaces. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25634-9_2
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