Arthur Wieferich

Arthur Josef Alwin Wieferich (* April 27, 1884 in Münster ( Westphalia ), † September 15, 1954 in Meppen ) was a German mathematician who published important work on number theory while studying.

Life

Wieferich was the son of a businessman. From 1903 to 1909 he studied at the Westfälische Wilhelms-Universität in Münster. Probably inspired him a lecture by Max Dehn in 1907 on number theory to further investigations in this field. In the time of the study were its five mathematical publications.

After graduating he taught as a school teacher in Konitz (then Poland), Elbing (West Prussia), Sopot (Baltic, now part of Poland ), Neustadt, Jülich, Stade and finally Meppen. At the same time, he was from 1909 to 1929 member of the German Mathematical Society (DMV). He married in 1916; his marriage remained childless. In Meppen, he was appointed at the time of the Nazis to the director of the high school in order to bring it to the party track. After the war he was suspended because of his Nazi past of this office and earned from 1945 to 1949 ( " denazification " time ) his living as a private tutor.

Work

Wieferich proved, among other things, is that if Fermat's Theorem for a prime p and integers prime to p fulfilled, this prime number p is a " Wieferich prime ", ie shares ( that p divides this term already implies the elementary " Fermat's little theorem "). Dmitry Mirimanoff showed that an appropriate sentence is true if 2 is replaced by 3 (criteria of Wieferich and Mirimanoff ). There are so far only two Wieferich prime numbers - 1093 and 3511 - known, and the search for such numbers has evolved into a sport with high-performance computers.

His sentence from the additive number theory about the representation of each integer from a maximum of 9 (positive) cubes gained the admiration of the then experts in this field, Edmund Landau in Göttingen. A gap ( Wieferich proved the theorem only from a certain limit ) in the proof was corrected by Aubrey J. Kempner in his dissertation, a further simplification is B. Scholz.

Writings

• Proof of the theorem that each integer can be represented as a sum of not more than nine positive cubes. Math Ann. Vol 66, 1908, pp. 95-101
• About the representation of numbers as sums of Biquadraten. Math Annals Vol 66, 1908, pp. 106-108
• To view the numbers as sums of fifth and seventh powers of positive integers. Math Ann. Vol 67 (1909 ) pp. 61-75
• To Fermat's Last Theorem. Journal of Pure and Applied Math Vol 136, 1909, pp. 293-302

• For the triangle geometry. Journal of Pure and Applied Math Vol 136, 1909, pp. 303-305