Brown number

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Brown numbers are pairs of whole numbers that are solutions to the Brocard problem, so that

n! + 1 = m2.

There are only three known pairs,

(4,5), (5,11), and (7,71)[1].

Paul Erdős conjectured that no other solutions exist. Most recently Bruce C. Berndt and William F. Galway performed calculations for n up to 109 and found no further solutions[2].

[edit] References

  1. ^ http://mathworld.wolfram.com/BrownNumbers.html
  2. ^ http://www.math.uiuc.edu/~berndt/articles/galway.pdf
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