7 problems

For every integer $n \ge 0$, every real number $K \ge 1$, and every nonempty set $A \subseteq \mathbb{F}_2^n$ satisfying $\lvert A+A\rvert \le K\lvert A\rvert$, there exist a subsp…

The supplied source identifies a source-corrected Written on the Wall II (WOWII) Graph Conjecture 160 and refers to an exact corrected statement, but does not provide that statemen…

The supplied source identifies this as a conjecture about finite graphs, with the relevant configuration involving a connected graph $G$ of radius $3$ having exactly one diametrica…

For every integer $k\ge 2$, the binomial-coefficient gcd quantity $D(k)$ specified in OEIS A080170 satisfies $D(k)=1$ if and only if…

Determine whether there exists an integer $n>24$ such that $\max_{1\le m<n}\bigl(m+\tau(m)\bigr)\le n+2$, where $\tau(m)$ denotes the number of positive divisors of $m$. Equivalent…

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Determine the normal orders of the arithmetic functions $h(n)$ and $H(n)$. The supplied source identifies this as Erdős Problem $\#696$, but does not define $h$, $H$, or specify th…