Roger Cotes' Formulas

Roger Cotes thoroughly investigated the factorization of x⁴ + a⁴. In doing so, he found the following formulas which he presented without proof:

Formula 1:


Formula 2:



Formula 3:



Formula 4:



These formulas demonstrated that Leibniz's supposition about x⁴ + a⁴ was incorrect.

The proof for these formulas would later be provided by Abraham de Moivre as he investigated the properties of the roots of unity.

References:

• Jean-Pierre Tignol, Galois' Theory of Algebraic Equations, World Scientific, 2001