• Corpus ID: 209367665

A nullstellensatz for sequences over F_p

  title={A nullstellensatz for sequences over F\_p},
  author={{\'E}ric Balandraud and Benjamin Girard},
. Let p be a prime and let A = ( a 1 ,...,a ℓ ) be a sequence of nonzero elements in F p . In this paper, we study the set of all 0-1 solutions to the equation a 1 x 1 + ··· + a ℓ x ℓ = 0 . We prove that whenever ℓ > p , this set actually characterizes A up to a nonzero multiplicative constant, which is no longer true for ℓ < p . The critical case ℓ = p is of particular interest. In this context, we prove that whenever ℓ = p and A is nonconstant, the above equation has at least p − 1 minimal 0… 

Representing Sequence Subsums as Sumsets of Near Equal Sized Sets

  • D. Grynkiewicz
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    Springer Proceedings in Mathematics & Statistics
  • 2021
For a sequence $S$ of terms from an abelian group $G$ of length $|S|$, let $\Sigma_n(S)$ denote the set of all elements that can be represented as the sum of terms in some $n$-term subsequence of



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THEOREM. Each set of 2n-1 integers contains some subset of n elements the sum of which is a multiple of n. PROOF. Assume first n = p (p prime). Our theorem is trivial for p = 2, thus henceforth p >

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The following theorem is proved. Ifa1,a2, ...an are nonzero elements inZn, and are not all equal, then ε1a1+ε2a2+...+εnan=0 has at leastn solutions with εi=0 or 1.

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  • Probab. Comput
  • 1999

Addendum to “The Critical Pairs of Subsets of a Group of Prime Order”

The Critical Pairs of Subsets of a Group of Prime Order

Historical note

  • P. Bucy
  • Medicine
    Surgical neurology
  • 1984

Cauchy Recherches sur les nombres

  • J. Ecole Polytech