Abstract
We state the following conjecture and prove it for the case whereq is a proper prime power:
Let A be a nonsingular n by n matrix over the finite field GFqq≧4, then there exists a vector x in (GFq)n such that both x and Ax have no zero component.
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References
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Research supported in part by Allon Fellowship and by a Bat Sheva de Rothschild grant.