A Property of Twin Primes
نویسندگان
چکیده
We determine the product of the invertible quadratic residues in Zn. This is a variation on Gauss’ generalization of Wilson’s Theorem. From this we deduce that for twin primes p, p + 2, the product of the invertible quadratic residues in Zp(p+2) is ±(p+1), where the sign depends on the residue class of p modulo 4. We examine necessary and sufficient conditions for consecutive odd natural numbers m,m+2 to satisfy this property of twin primes. The paper concludes with two open questions.
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