Wilhelm Ljunggren

Wilhelm Ljunggren (7 October 1905 – 25 January 1973) was a Norwegian mathematician, specializing in number theory.^[1]

Wilhelm Ljunggren

Career

Ljunggren was born in Kristiania and finished his secondary education in 1925. He studied at the University of Oslo, earning a master's degree in 1931 under the supervision of Thoralf Skolem, and found employment as a secondary school mathematics teacher in Bergen, following Skolem who had moved in 1930 to the Chr. Michelsen Institute there. While in Bergen, Ljunggren continued his studies, earning a dr.philos. from the University of Oslo in 1937.^[1][2]

In 1938 he moved to work as a teacher at Hegdehaugen in Oslo. In 1943 he became a fellow of the Norwegian Academy of Science and Letters, and he also joined the Selskapet til Vitenskapenes Fremme. He was appointed as a docent at the University of Oslo in 1948, but in 1949 he returned to Bergen as a professor at the recently founded University of Bergen. He moved back to the University of Oslo again in 1956, where he served until his death in 1973 in Oslo.^[1][2][3]

Research

Ljunggren's research concerned number theory, and in particular Diophantine equations.^[1] He showed that Ljunggren's equation,

X² = 2Y⁴ − 1.

has only the two integer solutions (1,1) and (239,13);^[4] however, his proof was complicated, and after Louis J. Mordell conjectured that it could be simplified, simpler proofs were published by several other authors.^[5][6][7]

Ljunggren also posed the question of finding the integer solutions to the Ramanujan–Nagell equation

2ⁿ − 7 = x²

(or equivalently, of finding triangular Mersenne numbers) in 1943,^[8] independently of Srinivasa Ramanujan who had asked the same question in 1913.

Ljunggren's publications are collected in a book edited by Paulo Ribenboim.^[9]