Abstrakt
Let tau(m,n) denote the maximal number of points on the discrete torus (discrete toric grid) of sizes m x n with no three collinear points. The value tau(m,n) is known for the case where gcd(m, n) is prime.
It is also known that tau(m,n) 1. In general, we do not know the period; however, if z = p(a) for p prime, then we can bound it.
We prove that tau(pa,p(a-1)p+2) = 2p(a) which implies that the period for the sequence is p(b), where b is at most (a - 1)p + 2.