Edward Waring, asks whether for every natural number $n$ there exists an associated positive integer s such that every natural number is the sum of at most $s$ $k$th powers of natural numbers ...
Suppose we have a circle of $2n$ people, where the first $n$ people are good guys and the people $n+1$ to $2n$ are bad guys. Can we always choose an integer $q$, such that if we execute successively ...
I recently was passing some time on Project Euler, when I came across this question. It deals with finding Pentagonal Numbers $P_j$ and $P_k$ such that $P_j+P_k$ and $P_j-P_k$ are also pentagonal ...