## 365 Citations

### Carmichael Meets Chebotarev

- MathematicsCanadian Mathematical Bulletin
- 2013

Abstract. For any finite Galois extension $K$ of $\mathbb{Q}$ and any conjugacy class $C$ in $\text{Gal}\left( {K}/{\mathbb{Q}}\; \right)$ , we show that there exist infinitely many Carmichael…

### Piatetski-Shapiro sequences

- Mathematics
- 2012

We consider various arithmetic questions for the Piatetski-Shapiro sequences bncc (n = 1, 2, 3, . . .) with c > 1, c 6∈ N. We exhibit a positive function θ(c) with the property that the largest prime…

### Carmichael Numbers with a Square Totient

- MathematicsCanadian Mathematical Bulletin
- 2009

Abstract Let $\varphi$ denote the Euler function. In this paper, we show that for all large $x$ there are more than ${{x}^{0.33}}$ Carmichael numbers $n\,\le \,x$ with the property that $\varphi…

### On the difficulty of finding reliable witnesses

- MathematicsANTS
- 1994

It is shown that there are finite sets of odd composites which do not have a reliable witness, namely a common witness for all of the numbers in the set.

### On Types of Elliptic Pseudoprimes

- Mathematicsjournal of Groups, Complexity, Cryptology
- 2021

We generalize the notions of elliptic pseudoprimes and elliptic Carmichael
numbers introduced by Silverman to analogues of Euler-Jacobi and strong
pseudoprimes. We investigate the relationships among…

### Carmichael Numbers for GL(m)

- Mathematics
- 2020

We propose a generalization of Carmichael numbers, where the multiplicative group Gm = GL(1) is replaced by GL(m) for m ≥ 2. We prove basic properties of these families of numbers and give some…

### Pseudoprosti brojevi

- 2020

Pitanje je li odre deni veliki prirodni broj n prost ili složen jedno je od najvažnijih u teoriji brojeva, a često se javlja na primjer u kriptografiji3 . U primjenama se najčešće zadovoljavamo…

### Millions of Perrin pseudoprimes including a few giants

- Computer Science, PhysicsArXiv
- 2020

It is thought that well over 90% of all 20-digit Perrin pseudoprimes are found, compared to the previously known just over 100,000, and two new sequences are proposed that do not provide any pseudopRimes up to $10^9$ at all.

### FACTORS OF CARMICHAEL NUMBERS AND AN EVEN WEAKER $k$ -TUPLES CONJECTURE

- MathematicsBulletin of the Australian Mathematical Society
- 2019

One of the open questions in the study of Carmichael numbers is whether, for a given $R\geq 3$ , there exist infinitely many Carmichael numbers with exactly $R$ prime factors. Chernick [‘On Fermat’s…

## References

SHOWING 1-10 OF 15 REFERENCES

### On Numbers Analogous to the Carmichael Numbers

- MathematicsCanadian Mathematical Bulletin
- 1977

A base a pseudoprime is an integer n such that 1 A Carmichael number is a composite integer n such that (1) is true for all a such that (a, n ) = l. It was shown by Carmichael [1] that, if n is a…