The recurrence relations for division polynomials of elliptic curves are well known: $$\Psi_{2n} = \Psi_n \left( \Psi_{n+2} \Psi_{n-1}^2 - \Psi_{n-2} \Psi_{n+1}^2 \right) / \ 2y$$ $$\Psi_{2n+1} = \Psi_{n+2} \Psi_n^3 - \Psi_{n+1}^3 \Psi_{n-1}$$

Who originally discovered these relations?

~~For some reason, a number of works do not cite the origin of the relations, e.g. Silverman's 2nd edition of ~~ See edit:*The Arithmetic of Elliptic Curves*, exercise 3.7 just gives them plainly.

SageMath cites Appendix A from Mazur-Tate from 1991 and they take a few pages to describe the discovery in full. However, they also show up in this paper (p.485, pdf p.4) from Schoof from 1985, citing Lang's
*Elliptic Curves; Diophantine Analysis* from 1978. Indeed, on page 37 of Lang we find the above result as Theorem 1.3, but again without a reference.

EDIT: I was wrong about Silverman not giving citations, they are just in the back of the book (p. 461) and he cites Lang, and also the same work by Cassels as given in the answer by Jeremy Rouse.