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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
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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