Corrigendum

Extract

J. W. S. Cassels, A note on the division values of ℘(u).

Monsieur Y. Hellegouarch has pointed out to me that the inequality (13₁) of my paper “A note on the division values of ℘ (u)” (Proc. Cambridge Phil. Soc.45 (1949), 169–172) does not follow from the argument hinted there and is almost certainly incorrect. All the argument shows is that the rather weaker estimate in (13₂) holds for m = p^k as well as for m = 2p^k.

The erroneous claim is reproduced in my report “Diophantine equations with special reference to elliptic curves” (J. London Math. Soc.41 (1966), 193–291) in expression (17.14) on page 247.