3 problems

Let $m_{k,n}(a,a)$ be the maximum size of a family of subsets of $[n]$ whose intersections are all congruent to $a$ modulo $k$, with $n\geq k\geq 2$. Parity conjecture. If…

Let $m_{k,n}(a,b)$ denote the maximum size of a family of subsets of $[n]$ whose pairwise intersections are congruent to $a$ modulo $k$ when the two subsets coincide and to $b$ mod…

Let $m_{k,n}(a,b)$ denote the maximum size of a family of subsets of $[n]$ whose pairwise intersections are congruent to $a$ modulo $k$ when the two subsets coincide and to $b$ mod…