3 problems

Ward's divisibility conjecture. Suppose that $p^e\mid d$ and $p^e\geq q$. Then $p^{e+1}/q$ is a divisor of $C$.

Divisible-set union conjecture. There exists a function $f\colon \mathbb{N}\to\mathbb{N}$ such that every $2^r$-divisible set of $f(r)\cdot [r+1]_2$ points over $\mathbb{F}_2$ is t…

Let $q$ be a prime power, let $r$ and $v$ be non-negative integers, and consider $q^r$-divisible spanning sets of $q^{r+1}$ points in $\operatorname{PG}(v-1,q)$. The generalized cy…