只有很大整数解的小丢番图方程组
Small systems of Diophantine equations which have only very large integer solutions
摘要：
设E_n={x_i=1，x_i+x_j=x_k，x_i \cdot x_j=x_k：i，j，k \in {1，.，n}}。存在一种算法，对于每个可计算函数f：N->N，该算法返回正整数m（f），对于该正整数m（f），第二算法接受输入f和任何整数n>=m（f），并且返回系统S \subseteq E_n，使得S具有无穷多个整数解并且每个整数元组（x_1，.，x_n）满足x_1=f（n）。对任意整数n>=12，我们构造一个系统S \subseteq E_n，使得S有无穷多个整数解，且它们都属于Z^n\[-2 ^<$2 ^{n-1}}，2 ^{2^{n-1}}]^n.
英文摘要：
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}}. There is an algorithm that for every computable function f:N->N returns a positive integer m(f), for which a second algorithm accepts on the input f and any integer n>=m(f), and returns a system S \subseteq E_n such that S has infinitely many integer solutions and each integer tuple (x_1,...,x_n) that solves S satisfies x_1=f(n). For each integer n>=12 we construct a system S \subseteq E_n such that S has infinitely many integer solutions and they all belong to Z^n\[-2^{2^{n-1}},2^{2^{n-1}}]^n.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
