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Date: 11-10-2020
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Date: 14-7-2020
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Date: 9-12-2020
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There are at least two Siegel's theorems. The first states that an elliptic curve can have only a finite number of points with integer coordinates.
The second states that if is an algebraic number of degree , then there is an depending only on such that
for all integer and (Landau 1970, pp. 37-56; Hardy 1999, p. 79).
REFERENCES:
Davenport, H. "Siegel's Theorem." Ch. 21 in Multiplicative Number Theory, 2nd ed. New York: Springer-Verlag, pp. 126-125, 1980.
Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, 1999.
Landau, E. Vorlesungen über Zahlentheorie, Vol. 3. New York: Chelsea, 1970.
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