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How Often is n! a Sum of Three Squares?

In: The Legacy of Alladi Ramakrishnan in the Mathematical Sciences

Author

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  • Jean-Marc Deshouillers

    (Université de Bordeaux et CNRS, IMB)

  • Florian Luca

    (Universidad Nacional Autónoma de México, Instituto de Matemáticas)

Abstract

Summary The positive integers n such that n! is a sum of three squares have a density which is equal to 7 ∕ 8. The key point for the proof of this result is to show that the above sequence is automatic and to study the matrix associated to the underlying automaton.

Suggested Citation

  • Jean-Marc Deshouillers & Florian Luca, 2010. "How Often is n! a Sum of Three Squares?," Springer Books, in: Krishnaswami Alladi & John R. Klauder & Calyampudi R. Rao (ed.), The Legacy of Alladi Ramakrishnan in the Mathematical Sciences, pages 243-251, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-6263-8_14
    DOI: 10.1007/978-1-4419-6263-8_14
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