Abstract :
We prove some partial results concerning the following problem:Assume that F is a finite field, aiis a complex number for each iset membership, variantF such that a0=0,a1=1, ai=1for all iset membership, variantF\{0},and∑iset membership, variantF ai+jimagei=−1for all iset membership, variantF\{0}.Does it follow that the function i→aiis a multiplicative character of F? We prove (in the case F=p,pis a prime) on the one hand that there is only a finite number of complex solutions; on the other hand we solve completely a mod pversion of the problem. The proofs are mainly elementary, except for applying a theorem of Chevalley from algebraic geometry
