Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T23:43:11.492Z Has data issue: false hasContentIssue false
  • English
  • Français

Sum of Two Fourth Powers of Integers

Published online by Cambridge University Press:  22 January 2016

Minoru Tsunekawa
Minoru Tsunekawa*
Affiliation:
Nagoya Institute of Technology
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Problems concerning the sum of two fourth powers of integers seem to be so difficult that little has been known since long years [3]. For instance, it is an important problem to determine whether there are infinitely many prime numbers which are represented in the form p = a4+b4. But nothing is known except that the density of such prime numbers is easily proved to be 0; accordingly it is difficult to obtain a necessary and sufficient condition under which p is represented in such a form.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 18 , April 1961 , pp. 53 - 61
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1961

References

[1] Kuroda, S., Über den Dirichletschen Körper, Jour, of the Faculty of Science, University of Tokyo, Sec 1, vol. IV, Part 5(1943), pp. 384–393.Google Scholar
[2] Takagi, T., Daisûteki Seisûron (The theory of algebraic numbers), Tokyo, 1948.Google Scholar
[3] Dickson, L. E., History of the theory of numbers, vol. 2(1920), pp. 644–648.Google Scholar