Mordell curve

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k=1

In mathematics, a Mordell curve is an elliptic curve

y² = x³ + k,

with k an integer. These curves were closely studied by Louis Mordell, from the point of view of determining their integer points. He showed that for k fixed there are only finitely many solutions (x,y) in integers.

In other words, the differences of perfect squares and perfect cubes tend to ∞. 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.