2 problems

Let a semiprime be a product $m=pq$ of two, not necessarily distinct, primes. For each $x\geq 1$, consider the semiprimes $m\leq x$ and compare those whose two prime factors satisf…

Let $\frac{a}{b}$ be a positive rational number with squarefree denominator $b$. An Egyptian-fraction representation is a sum of distinct unit fractions whose denominators are prod…