The Ramanujan Journal

, Volume 4, Issue 1, pp 41–42

On the Brocard–Ramanujan Diophantine Equation n! + 1 = m2

  • Bruce C. Berndt
  • William F. Galway
Article

Abstract

In 1876, H. Brocard posed the problem of finding all integral solutions to n! + 1 = m2. In 1913, unaware of Brocard's query, S. Ramanujan gave the problem in the form, “The number 1 + n! is a perfect square for the values 4, 5, 7 of n. Find other values.” We report on calculations up to n = 109 and briefly discuss a related problem.

diophantine equations ABC conjecture 

References

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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Bruce C. Berndt
    • 1
  • William F. Galway
    • 2
  1. 1.Department of MathematicsUniversity of IllinoisUrbana
  2. 2.Department of MathematicsUniversity of IllinoisUrbana

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