Wilhelm Ljunggren

Wilhelm Ljunggren (born October 7, 1905 in Oslo ; † January 25, 1973 there ) was a Norwegian mathematician.

Ljunggren's father was a wheelwright and was originally from Sweden. Ljunggren's mathematical talent was already evident at school, where he received the Crown Prince Olav Prize for the student who best solved mathematical problems from the Norsk Matematisk Tidsskrift. Later he was also very interested in solving and composing problems for magazines. He studied mathematics and especially number theory with Thoralf Skolem at the University of Oslo . When Skolem went to Bergen in 1930 he was followed by Ljunggren, who accepted a position as a high school teacher there. In 1937 he received his doctorate in Oslo and when Skolem became a professor in Oslo in 1938, Ljunggren followed him there and became a teacher at the Hegedehaugen School. In 1948 he became associate professor in Oslo and in 1949 professor at the University of Bergen, founded in 1946. In 1956 he became a professor at the University of Oslo, but also taught at the technical institute.

Ljunggren dealt with Diophantine equations , especially fourth degree. A Diophantine equation named after him is:

{\ displaystyle x ^ {2} = 2y ^ {4} -1}

As a curve, it corresponds to an elliptical curve. Ljunggren proved that the only integer solutions are (1,1) and (239, 13). The equation gives the cases of the star tetrahedron numbers (stella octangula), which are squares. They satisfy the equation , which can be transformed into Ljunggren's equation. ${\ displaystyle m ^ {2} = n (2n ^ {2} -1)}$

He had been married to Else Margrethe Aas since 1950.

He was a member of the Norwegian Academy of Sciences.

Fonts

Paulo Ribenboim (Ed.): Collected papers of Wilhelm Ljunggren, Queen's papers in pure and applied mathematics, 115, Kingston, Ontario: Queen's University, 2003

Web links

John J. O'Connor, Edmund F. Robertson : Wilhelm Ljunggren. In: MacTutor History of Mathematics archive .

Individual evidence

↑ Ljunggren, On The Theory of the Equation , Avh. Norske Vid. Akad. Oslo. I., 1942 (5), p. 27 ${\ displaystyle x ^ {2} + 1 = Dy ^ {4}}$
↑ Stella Octangula Number , mathworld

personal data
SURNAME	Ljunggren, Wilhelm
BRIEF DESCRIPTION	Norwegian mathematician
DATE OF BIRTH	October 7, 1905
PLACE OF BIRTH	Oslo
DATE OF DEATH	January 25, 1973
Place of death	Oslo

[1] Ljunggren, On The Theory of the Equation , Avh. Norske Vid. Akad. Oslo. I., 1942 (5), p. 27 ${\ displaystyle x ^ {2} + 1 = Dy ^ {4}}$

[2] Stella Octangula Number , mathworld