BIT Numerical Mathematics

, Volume 11, Issue 2, pp 212–216 | Cite as

On a conjecture by Erdös-Straus

  • D. G. Terzi
Article
  • 39 Downloads

Abstract

Two algorithms have been constructed. The first is intended for obtaining such residue-classes represented by the numberN to the given modulusM, that for the primenN (modM) equation (1) is solvable in natural numbersx,y,z. Particularly, whenM=120120 (see Table 2) we obtain 198 suchN, i.e. the hypothesis indicated below is true with a probability greater than 0.99835. The second algorithm is intended for testing the conjecture by Erdös-Straus when 107 <n≦108.

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References

  1. 1.
    L. J. Mordell,Diophantine equations, London · New York, Acad. Press, 1969.Google Scholar
  2. 2.
    Г. Дэвенпорт,Высuаaя арuфмеmuкa, Москва, 1965.Google Scholar
  3. 3.
    L. Antonio Rosati,Sull'equazione diofantea 4/n=1/x 1+1/x 2+1/x 3, Bolettino della Unione Matematica Italiana, serie III, Anno IX (1954), No. 1.Google Scholar
  4. 4.
    L. Bernstein,Zur Lösung der diophantischen Gleichung m/n=l 1 x+l 2 y+l 3 z,insbesondere im Fall m=4, J. reine und angew. Math., 1962, 211, No. 1–2.Google Scholar
  5. 5.
    Koichi Yamomoto,On the diophantine equation 4/n=1/x+1/y+1/z, Mem. Fac. Sci. Kyushu Univ., 1965, A19, No.1.Google Scholar

Copyright information

© BIT Foundations 1971

Authors and Affiliations

  • D. G. Terzi
    • 1
  1. 1.Institute of Mathematics Siberian BranchAcademy of Sciences of the UssrNovosibirsk 90Ussr

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