We say that two vectors of integers a, u are coprime if the positive integers ||a||^2, ||u||^2 are coprime. We will prove that if M > 1 is a positive integer, the three following propositions are equivalent: 1) M is prime; 2) Each vector a of Z^4 such that ||a||^2 = M is coprime to each vector u of Z^4, u != 0, ||u||^2 < M and u orthogonal to a; 3) There exists a vector a of Z^4 with ||a||^2 = M such that a is coprime to each vector u of Z^4, u != 0, ||u||^2 < M and u orthogonal to a.
C. Tinaglia (2004). On a Geometric Characterization of Rational Prime Integer. BOLOGNA : Tecnoprint.
On a Geometric Characterization of Rational Prime Integer
TINAGLIA, CALOGERO
2004
Abstract
We say that two vectors of integers a, u are coprime if the positive integers ||a||^2, ||u||^2 are coprime. We will prove that if M > 1 is a positive integer, the three following propositions are equivalent: 1) M is prime; 2) Each vector a of Z^4 such that ||a||^2 = M is coprime to each vector u of Z^4, u != 0, ||u||^2 < M and u orthogonal to a; 3) There exists a vector a of Z^4 with ||a||^2 = M such that a is coprime to each vector u of Z^4, u != 0, ||u||^2 < M and u orthogonal to a.File in questo prodotto:
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