PORTUGALIAE MATHEMATICA Vol. 56, No. 3, pp. 257263 (1999) 

Primitive Quadratics Reflected in $B_{2}$SequencesBernt LindströmDepartment of Mathematics, Royal Institute of Technology,S100 44 Stockholm  SWEDEN Abstract: A $B_{2}$sequence of positive integers $a_{1},a_{2},...,a_{r}$ has the property that the sums $a_{i}+a_{j}$, $1\le i\le j\le r$, are different. R.C. Bose and S. Chowla have proved the existence of $B_{2}$sequences of size $r=q$, a power of a prime $p$, such that the sums $a_{i}+a_{j}$, $1\le i\le j\le r$, are different modulo $q^{2}1$. If $\theta\in GF(q^{2})$ is a primitive element, then $A(q,\theta)=\{a\dpt 1\le a<q^{2}1$, $\theta^{a}\theta\in GF(q)\}$ gives a BoseChowla sequence. Classification (MSC2000): 11B50, 11B83, 11T06. Full text of the article:
Electronic version published on: 31 Jan 2003. This page was last modified: 27 Nov 2007.
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