ABSTRACT: We prove that all irreducible but solvable equations of degree n can be transformed in radicals into the binomial form y^n+c=0 using a Tschirnhausen transformation of degree n-1. The resulting equation is then solvable by a single nth root extraction. In particular, we illustrate the method using the solvable quintic.
Mathematics Subject Classification. Primary: 12E12; Secondary: 12F10
ABSTRACT: We explore a hitherto unsuspected connection between certain solvable quintics with rational coefficients whose parametrization involves Fibonacci numbers as a particular case, but entails the solution of the Pell equation x^2-Dy^2 = 4 in the general case. An additional connection to Pythagorean triples will also be discussed.
Mathematics Subject Classification: Primary: 12E12; Secondary: 11D09.
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