By coincidence, the April 2002 issue of the Mathematics Magazine arrived at

my house yesterday and the lead article discusses the many applications of

the 7-et set. One of the first theorems inthe article is that if p is a

prime of the form 4n+3, then the squares mod p will give you a set of

2n+1 elements where each difference occurs n times. So for 19 we have the

set {1, 4, 5, 6, 7, 9, 11, 16, 17} where each difference occurs 4 times and

for 31 we have the set {1, 2, 4, 5, 7, 8, 9, 10, 14, 16, 18, 19, 20, 25, 28}

where each difference occurs 7 times.

David Bowen