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Diophantine Set

المؤلف:  Ribenboim, P.

المصدر:  The New Book of Prime Number Records. New York: Springer-Verlag

الجزء والصفحة:  pp. 189-192

24-5-2020

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Diophantine Set

A set  of positive integers is said to be Diophantine iff there exists a polynomial  with integral coefficients in  indeterminates such that

{Q(x_1,...,x_m)>=1:x_1>=1,...,x_m>=1}. " src="https://mathworld.wolfram.com/images/equations/DiophantineSet/NumberedEquation1.gif" style="height:15px; width:252px" />

It has been proved that the set of prime numbers is a Diophantine set.

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REFERENCES:

Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, pp. 189-192, 1995.