Sum of two repdigits a square
  A \emph{repdigit} is a natural number greater than 10 which has all of its base-10 digits the same. In this paper we find all examples of two repdigits adding to a square. The proofs lead to interesting questions about consecutive quadratic residues and non-residues, and provide an elementary application of elliptic curves. 
Bart Goddard, Jeremy Rouse
math.NT