$S$-prime numbers Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource
Let $S$ be the set of all positive integers that are $1$ more than a multiple of $10$, so $S = \{1, 11, 21, 31, 41, \dotsc\}$.
We say that an element $x$ of the set $S$ is $S$-prime if $x > 1$ and whenever the elements $a$ and $b$ of the set $S$ satisfy $ab = x$ we have $a = 1$ or $b = 1$.
Are there distinct $S$-prime numbers $a$, $b$, $c$ and $d$ such that $ab = cd$?