Mordell curve
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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.
[edit] Reference
- Louis Mordell, Diophantine Equations (1969)
