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- What are primitive roots modulo n? - Mathematics Stack Exchange
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- proof: primitive pythagorean triple, a or b has to be divisible by 3
Both s and t cannot be multiples of 3, as that will cause both a and b to be multiples of 3 and the triplet won't be primitive If neither s nor t is a multiple of 3
- Show that $2$ is a primitive root modulo $13$.
I thought $\varphi (12)$ counts the number of coprimes to $12$ Why does this now suddenly tell us the number of primitive roots modulo $13$? How have these powers been plucked out of thin air? I understand even powers can't be primitive roots, also we have shown $2^3$ can't be a primitive root above but what about $2^9$?
- Every primitive matrix is irreducible? - Mathematics Stack Exchange
A nonnegative, irreducible matrix is primitive if and only if it is aperiodic (ibid Theorem 8 5 3) According to this source, we wouldn't ever call a reducible matrix primitive Though a reducible matrix can still have a simple maximal modulus eigenvalue, e g the zero matrix with a lone positive number at one location in the diagonal
- Finding a primitive root of a prime number
How would you find a primitive root of a prime number such as 761? How do you pick the primitive roots to test? Randomly? Thanks
- Proof of existence of primitive roots - Mathematics Stack Exchange
Proof of existence of primitive roots Ask Question Asked 11 years, 6 months ago Modified 11 years, 6 months ago
- Primitive $p$-th root of unity with characteristic $p$
Leaving field theory again, if we consider the different complex roots of the polynomials $\alpha_i$ (excluding non-primitive root $1$, we would have $1\leq i \leq p-1$)
- Primitive binary necklaces - Mathematics Stack Exchange
The problem solution of counting the number of (primitive) necklaces (Lyndon words) is very well known But what about results giving sufficient conditions for a given necklace be primitive? For ex
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