Sum of two repdigits a square
Bart Goddard, Jeremy Rouse
TL;DR
This paper classifies all pairs of repdigit numbers whose sum is a perfect square, using elementary methods and elliptic curves, and explores related questions in number theory.
Contribution
It provides a complete characterization of repdigit pairs summing to squares and introduces novel elementary and elliptic curve techniques for this problem.
Findings
Identifies all repdigit pairs summing to a perfect square
Connects the problem to properties of quadratic residues and elliptic curves
Offers new insights into the structure of repdigits and squares
Abstract
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.
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Taxonomy
TopicsCryptography and Residue Arithmetic · Polynomial and algebraic computation · Algebraic Geometry and Number Theory