Mathematical Notes

, Volume 88, Issue 3–4, pp 599–602 | Cite as

A supercongruence motivated by the Legendre family of elliptic curves

  • Heng Huat Chan
  • Ling Long
  • V. V. Zudilin


A new supercongruence associated with a Gaussian hypergeometric series, as well as one of Mortenson’s supercongruences, are established with new congruence relations and the Legendre transforms of certain sequences.

Key words

elliptic curve ramified double cover finite field Hasse invariant supercongruence Legendre transform 


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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.National University of SingaporeSingaporeSingapore
  2. 2.Iowa State UniversityIowaUSA
  3. 3.University of NewcastleNewcastleAustralia

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