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For prime p and 1 ≤ a, b, c < p let V be the algebraic set of the congruence ax − by ≡ c (mod p) in the plane. For an arbitrary box of size B we obtain a necessary and a sufficient conditions on the size B in order for the box to meet V. For arbitrary subsets S, T of Zp we also obtain a necessary and a sufficient conditions on the cardinalities of S, T so that S + T = Zp.
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Cite this paper
Ayyad, A. (2016). On the congruence ax −by ≡ c (mod p) and the finite field Zp. Notes on Number Theory and Discrete Mathematics, 22(1), 29-32.