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math.NT2016
Quadratic forms representing all integers coprime to 3
Justin DeBenedetto, Jeremy Rouse
Following Bhargava and Hanke's celebrated 290-theorem, we prove a universality theorem for all positive-definite integer-valued quadratic forms that represent all positive integers…
math.NT2016
When is the sum of two squares?
Greg Dresden, Kylie Hess, Saimon Islam +5
Using Fermat's two squares theorem and properties of cyclotomic polynomials, we prove assertions about when numbers of the form can be expressed as the sum of two integer…
math.NT2016
Sum of two repdigits a square
Bart Goddard, Jeremy Rouse
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 proo…