Trygve Nagell

Trygve Nagell (July 13, 1895 in Oslo – January 24, 1988 in Uppsala) was a Norwegian mathematician, known for his works on the Diophantine equations within number theory.[1]

Trygve Nagell in the 1930s.

Education and career

He received his doctorate at the University of Oslo in 1926, and lectured at the University until 1931. He was a professor at the University of Uppsala from 1931 to 1962.[2] His doctoral students include Harald Bergström.

Contributions

Nagell proved a conjecture of Srinivasa Ramanujan that there are only five numbers that are both triangular numbers and Mersenne numbers. They are the numbers 0, 1, 3, 15, and 4095. The formula expressing the equality of a triangular number and a Mersenne number can be simplified to the equivalent form

2^{n}-7=x^{2},

which likewise has five solutions in natural numbers $n$ and $x$ , with solutions for $n\in \{3,4,5,7,15\}$ . In honor of Nagell's solution, this equation is called the Ramanujan–Nagell equation.[3]

The Nagell–Lutz theorem is a result in the diophantine geometry of elliptic curves, which describes rational torsion points on elliptic curves over the integers. It was published independently by Nagell and by Élisabeth Lutz.[4]

Awards and honors

Nagell was appointed Commander of the Royal Norwegian Order of St. Olav in 1951, and of the Swedish Order of the Polar Star in 1952.[1]

References

Ellingsrud, Geir. "Trygve Nagell". In Helle, Knut (ed.). Norsk biografisk leksikon (in Norwegian). Oslo: Kunnskapsforlaget. Retrieved 2 September 2009.
Henriksen, Petter, ed. (2007). "Trygve Nagell". Store norske leksikon (in Norwegian). Oslo: Kunnskapsforlaget. Retrieved 2 September 2009.
Turnwald, Gerhard (1990). "A note on the Ramanujan-Nagell equation". Number-theoretic analysis (Vienna, 1988–89). Lecture Notes in Math. 1452. Springer, Berlin. pp. 206–207. doi:10.1007/BFb0096992. MR 1084649.
Silverman, Joseph H.; Tate, John T. (2015). "2.5 The Nagell–Lutz theorem and further developments". Rational points on elliptic curves. Undergraduate Texts in Mathematics (2nd ed.). Cham: Springer. pp. 56–58. doi:10.1007/978-3-319-18588-0. ISBN 978-3-319-18587-3. MR 3363545.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.

[nbl-1] Ellingsrud, Geir. "Trygve Nagell". In Helle, Knut (ed.). Norsk biografisk leksikon (in Norwegian). Oslo: Kunnskapsforlaget. Retrieved 2 September 2009.

[snl-2] Henriksen, Petter, ed. (2007). "Trygve Nagell". Store norske leksikon (in Norwegian). Oslo: Kunnskapsforlaget. Retrieved 2 September 2009.

[3] Turnwald, Gerhard (1990). "A note on the Ramanujan-Nagell equation". Number-theoretic analysis (Vienna, 1988–89). Lecture Notes in Math. 1452. Springer, Berlin. pp. 206–207. doi:10.1007/BFb0096992. MR 1084649.

[4] Silverman, Joseph H.; Tate, John T. (2015). "2.5 The Nagell–Lutz theorem and further developments". Rational points on elliptic curves. Undergraduate Texts in Mathematics (2nd ed.). Cham: Springer. pp. 56–58. doi:10.1007/978-3-319-18588-0. ISBN 978-3-319-18587-3. MR 3363545.