$a_n$ is a non-decreasing sequence of positive integers. If an positive integer $k$ appears in $a_n$ exactly $k$ times and $S_n$ is the sum of the first n terms, find all $N$ such that $S_N$ is prime. ...
$T_n$ is the $n$-th triangular number,
show that there are
an infinite number of positive integers
$a, b, c, d$
for all $n$.
This is inspired
by an article in ...