1. CMB 2014 (vol 57 pp. 551)
2. CMB 2005 (vol 48 pp. 211)
 Germain, Jam

The Distribution of Totatives
The integers coprime to $n$ are called the {\it totatives} \rm of $n$.
D. H. Lehmer and Paul Erd\H{o}s were interested in understanding when
the number of totatives between $in/k$ and $(i+1)n/k$ are $1/k$th of
the total number of totatives up to $n$. They provided criteria in
various cases. Here we give an ``if and only if'' criterion which
allows us to recover most of the previous results in this literature
and to go beyond, as well to reformulate the problem in terms of
combinatorial group theory. Our criterion is that the above holds if
and only if for every odd character $\chi \pmod \kappa$ (where
$\kappa:=k/\gcd(k,n/\prod_{pn} p)$) there exists a prime $p=p_\chi$
dividing $n$ for which $\chi(p)=1$.
Categories:11A05, 11A07, 11A25, 20C99 

3. CMB 2004 (vol 47 pp. 358)
 Ford, Kevin

A Strong Form of a Problem of R. L. Graham
If $A$ is a set of $M$ positive integers, let $G(A)$ be the maximum
of $a_i/\gcd(a_i,a_j)$ over $a_i,a_j\in A$. We show that if
$G(A)$ is not too much larger than $M$, then $A$ must have a
special structure.
Category:11A05 

4. CMB 2002 (vol 45 pp. 109)
 Hall, R. R.; Shiu, P.

The Distribution of Totatives
D.~H.~Lehmer initiated the study of the distribution of totatives, which
are numbers coprime with a given integer. This led to various problems
considered by P.~Erd\H os, who made a conjecture on such distributions.
We prove his conjecture by establishing a theorem on the ordering of
residues.
Keywords:Euler's function, totatives Categories:11A05, 11A07, 11A25 
