Counting integers representable as images of polynomials modulo n
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Date
2019
Authors
Arias, Fabián
Borja, Jerson
Rubio, Luis
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Abstract
Given a polynomial f(x1,x2,…,xt) in t variables with integer coefficients and a positive integer n, let α(n) be the number of integers 0 ≤ a < n such that the polynomialcongruencef(x1,x2,…,xt) ≡ a(modn)issolvable. Wedescribeamethod that allows us to determine the function α associated with polynomials of the form c1xk1+c2xk2+···+ctxkt. Then, we apply this method to polynomials that involve sums and differences of squares, mainly to the polynomials x2 +y2, x2 −y2, and x2 +y2 +z2. © 2019, University of Waterloo. All rights reserved.
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Arias, F., Borja, J., & Rubio, L. (2018). Counting integers representable as images of polynomials modulo $ n$. arXiv preprint arXiv:1812.11599.