4 problems

Let $\lambda(n)$ be the Carmichael lambda function, defined as the exponent of $(\mathbb{Z}/n\mathbb{Z})^{\times}$, and define its iterates by … Let $L(n)$ be the smallest non-nega…

Let $\lambda$ denote Carmichael's lambda function, and call an integer $m$ a value of $\lambda$ if $m=\lambda(k)$ for some positive integer $k$. Range-square conjecture. Asymptotic…

Let $p,q,r,s$ denote primes. For a prime $q$, construct a tree $T(q)$ rooted at $q$ by linking each prime power $p^e$ exactly dividing $q-1$ to $q$, and recursively linking each…

Let $\lambda(n)$ be the Carmichael function, the largest order of any number modulo $n$. Banks–Ford–Luca conjecture. For every positive integer $n$, there is an integer $m\ne n$ wi…