Small systems of Diophantine equations with a prescribed number of solutions in non-negative integers

Details Small systems of Diophantine equations with a prescribed number of solutions in non-negative integers Small systems of Diophantine equations with a prescribed number of solutions in non-negative integers

2011-10-17

arxiv.org/abs/1110.3549v16

Mathematics

Logic

10 pages, minor changes

Scientific paper

Let E_n={x_i=1, x_i+x_j=x_k, x_i \cdot x_j=x_k: i,j,k \in {1,...,n}}. If
Matiyasevich's conjecture on single-fold Diophantine representations is true,
then for every computable function f:N->N there is a positive integer m(f) such
that for each integer n>=m(f) there exists a system U \subseteq E_n which has
exactly f(n) solutions in non-negative integers x_1,...,x_n.

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