Published June 8, 2023 | Version MUST
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Brocard's problem proof and the solutions of the diophantine Ramanujan's equation

Authors/Creators

  • 1. École normale supérieure-kouba- Alger

Description

In this paper we give a conclusive proof of BROCARD'S stuck history problem until moment. The idea of proof be clear when we found a simular formula to BROCARD'S équation ( Pythagorean equation) that led us to geometry which was the hidden piece that revealed the mystery from the problem by using reduction to absurdity, After that we generalized this method to study the RAMANUJAN diophantine equation.

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References

  • R.K. Guy , Unsolved Problems in Number Theory, third Ed. Problem Books in Math, Spriger-Verlag , New York , 2004.
  • . Brocard, Question 166. Nouveau. Corresponding. Math. 2 (1876) 287.
  • H. Brocard, Question 1532, Nouveau. Ann. Math. 4 (1885) 291.
  • R.K. Guy , Unsolved Problems in Number Theory, third Ed. Problem Books in Math, Spriger-Verlag , New York , 2004.