Dissections of triangles and distances of groups

Denote by gdist(p) the least number of cells that have to be changed to get a latin square from the table of addition modulo prime p. A conjecture of Drápal, Cavenagh and Wanless states that there exists c > 0 such that gdist(p) ≤ c log(p). In this work we prove the conjecture for c ≈ 7.21, and the proof is done by constructing a dissection of an equilateral triangle of side n into O(log(n)) equilateral triangles. We also show a proof of the lower bound c log(p) ≤ gdist(p) with improved constant c ≈ 2.73. At the end of the work we present computational data which suggest that gdist(p)/ log(p) ≈ 3.56 for large values of p