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SHORTEST DISTANCE IN MODULAR HYPERBOLA AND LEAST QUADRATIC NON‐RESIDUE
Author(s) -
Chan Tsz Ho
Publication year - 2016
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579316000073
Subject(s) - hyperbola , mathematics , quadratic residue , residue (chemistry) , quadratic equation , square (algebra) , modular design , combinatorics , legendre symbol , geometry , quadratic function , quadratic field , biochemistry , chemistry , computer science , operating system
In this paper, we study how small a box contains at least two points from a modular hyperbola x y ≡ c ( mod p ) . There are two such points in a square of side lengthp 1 / 4 + ∈. Furthermore, it turns out that either there are two such points in a square of side lengthp 1 / 6 + ∈or the least quadratic non‐residue is less thanp 1 / ( 6 e ) + ∈.
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