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I think I am able to prove the following result which gives a partial answer to my question. Theorem: Let $n \ge 3$ and $d > n/2$. Then $\alpha_n^d$ (the number of zero-sum free $d$-tuples in $\math …

Let $n$ and $d$ be positive integers. Define $\alpha_n^d$ to be the number of vectors $(x_1, x_2, \cdots, x_d)$ in $\mathbb{Z}_n^d$ such that given any subset $S$ of $\{ 1, 2, 3, \cdots d\}$, $\sum_{ …

I am proposing (and will be teaching next year) a new math elective on Cryptography in our curriculum here at Illinois State University. In addition to standard topics including RSA public key and ell …

I am looking for a good textbook suitable for graduate or advanced undergraduate students who want to explore algorithmic number theory. Specifically, algorithms for primality testing, and factoring …

I am writing a paper in which I keep referring to primes p for which 2 is a primitive root mod p and so I want to give a name for these primes. Is there a name for these primes in the literature alre …

Let $F$ be a infinite field of characteristic 2 whose multiplicative group $F^*$ is torsion free. I would like to conclude that $F^*$ is decomposable or find an example where $F^*$ is indecomposable. …