Maximal Residue Difference Sets Modulo p

Twelfth Power Qualified Residue Difference Sets

Qualified residue difference sets of power n are known to exist for n = 2, 4, 6, as do similar sets that include the zero element, while both classes of set are known to be nonexistent for n = 8 and n = 10. Both classes of set are proved nonexistent for n = 12.

On sum-free sets modulo p

Let p be a sufficiently large prime and A be a sum-free subset of Z/pZ; improving on a previous result of V. F. Lev, we show that if |A| = card(A) > 0.324p, then A is contained in a dilation of the interval [|A| , p− |A|] (mod. p).

Distribution of Difference between Inverses of Consecutive Integers modulo P

Let p > 2 be a prime number. For each integer 0 < n < p, define n by the congruence nn ≡ 1 (mod p) with 0 < n < p. We are led to study the distribution behavior of n− n+ 1 in order to prove the asymptotic formula p−2 ∑ n=1 |n− n+ 1| = 1 3 p +O(p log p).

Some results on maximal open sets

In this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. Some results about existence of maximal m-open setsare given. Moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.Our results are supported by examples and counterexamples.

REDUCTION MODULO pn OF p -ADIC SUBANALYTIC SETS