تسجيل الدخول

تسجيل

Prime Diophantine Equations

المؤلف:  Jones, J. P.; Sato, D.; Wada, H.; and Wiens, D.

المصدر:  "Diophantine Representation of the Set of Prime Numbers." Amer. Math. Monthly 83

الجزء والصفحة:  ...

7-6-2020

1328

Prime Diophantine Equations

 is prime iff the 14 Diophantine equations in 26 variables

	(1)
	(2)
	(3)
	(4)
	(5)
	(6)
	(7)
	(8)
	(9)
	(10)
{[a+u^2(u^2-a)]^2-1}(n+4dy)^2+1-(x+cu)^2=0 " src="https://mathworld.wolfram.com/images/equations/PrimeDiophantineEquations/Inline12.gif" style="height:22px; width:312px" />	(11)
	(12)
	(13)
	(14)

have a solution in positive integers (Jones et al. 1976; Riesel 1994, p. 40).

---

REFERENCES:

Jones, J. P.; Sato, D.; Wada, H.; and Wiens, D. "Diophantine Representation of the Set of Prime Numbers." Amer. Math. Monthly 83, 449-464, 1976.

Riesel, H. Prime Numbers and Computer Methods for Factorization, 2nd ed. Boston, MA: Birkhäuser, 1994.