Lucas's proof of a special case of Beal's conjecture While studying the properties of a certain elliptic curve, I came across the equation $x^4+y^4=z^3$. There is no solution of this equation in relatively prime integers, and this is a special case of Beal's conjecture. According to this source, the proof that $x^4+y^4=z^3$ has no solutions in relatively prime integers was given by Lucas in the 19th century. Does anyone have a reference which links to Lucas's proof (or even a document which gives a proof sketch)?

The following answer to my question was possible thanks to the links which Mike Miller gave. On page 630 of Dickson's "History of the Theory of Numbers", the following is written: "E. Lucas listed and treated the solvable equations $ax^4+by^4=cz^2$" in which $2$ and $3$ are the only primes dividing $a,b$, or $c$, viz." (he then lists out a bunch of values for $(a,b,c)$). In the fifth section of the second link (this), the relation between Lucas's work and the solutions to the equation $x^4+y^4=z^3$ is given. This is possible because of a certain change of variables which reduces to studying equations of the form $ax^4+by^4=cz^2$, and Lucas's theorem can be applied here.