2 problems

For integers $n,k\geq 1$, define $C_n$ to be the set of $kn$-bit binary $k$th powers … so that $C_n$ has cardinality $2^{n-1}$. For sets $S$ and $T$, their sumset is…

A natural number is a binary cube if it is a power of two raised to the third power. Nine binary cubes conjecture. Every natural number greater than $147615$ is the sum of at most…