1. Introduction. By a famous theorem of Siegel [S], the number of integral points on an elliptic curve E over an algebraic number field K is finite. A conjecture of Lang and Demyanenko (see [L3], p. 140) states that, for a quasiminimal model of E over K, this number is bounded by a constant depending only on the rank of E over K and on K (see also [HSi],… (More)
We completely solve diophantine equations of the form Y 2 = X 3 ± p k X, where k is a positive integer, using a reduction to some quartic elliptic equations, which can be solved with well known methods.