Mordell curve

In algebra, a Mordell curve is an elliptic curve of the form y² = x³ + n, where n is a fixed non-zero integer.^[1]

These curves were closely studied by Louis Mordell,^[2] from the point of view of determining their integer points. He showed that every Mordell curve contains only finitely many integer points (x, y). In other words, the differences of perfect squares and perfect cubes tend to infinity. The question of how fast was dealt with in principle by Baker's method. Hypothetically this issue is dealt with by Marshall Hall's conjecture.