1. CMB Online first
 Wright, Thomas

Variants of Korselt's Criterion
Under sufficiently strong assumptions about the first term in
an arithmetic progression, we prove that for any integer $a$,
there are infinitely many $n\in \mathbb N$ such that for each
prime factor $pn$, we have $pana$. This can be seen as a
generalization of Carmichael numbers, which are integers $n$
such that $p1n1$ for every $pn$.
Keywords:Carmichael number, pseudoprime, Korselt's Criterion, primes in arithmetic progressions Category:11A51 

2. CMB 2007 (vol 50 pp. 158)
 Tipu, Vicentiu

A Note on Giuga's Conjecture
Let $G(X)$ denote the number of positive composite integers $n$
satisfying $\sum_{j=1}^{n1}j^{n1}\equiv 1 \tmod{n}$.
Then $G(X)\ll X^{1/2}\log X$ for sufficiently large $X$.
Category:11A51 
